From cb58cd7eadf74a4dd46c83bc64447a3810876a0a Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Fri, 31 Jul 2026 13:13:03 +0200 Subject: [PATCH 01/22] Round-4 TSI report review: apply findings, editorial pass, code + figure fixes Applied the reconstructed round-4 review to the TSI parameter-selection report set (reports/tsi) and executed the follow-ups. Report (reports/tsi): - Applied the must+should findings across README + parts 1-4: cross-part numeric corrections, figure-caption fixes, spec reconciliation, and cross-file companions (hops-degradation and notch/reward numbers, tip-agreement ordering, density-window timing, VRF -> ZK Proof-of-Leadership, w_u window/reward gloss). - Editorial pass for timeless voice (no "now adopted / merged / coin" narration) and a gentle spec-safety framing (recommendations are thresholds; the protocol's MAX_UNCLES=4 sits safely above them). - Added the fork-rate-vs-scale table (6.10), defined "grinding gain", promoted the clock-skew study to its own paragraph, added the correlated-latency caveat, and moved fig27/fig28 beside their discussion. - Documented the Blend cascade in 2: hops propagate over the shared gossip graph (not direct links), the final broadcast comes from the last relay, relays are blind forwarders. Simulator (tools/simulators/tsi/tsi-sim-pernode): - Docstring/dead-code fixes: theory.block_count_ceiling (legacy framing), measure, reorg (catch-up reading), metrics (removed two dead helpers), config (fixed_point 10^-6; clock_skew_max/lottery_chunks documented inert), stake_vs_delay. - Generator correctness + regenerated figures: figures_pernode.CONFIG_COLS now exhaustive (f no longer pooled); rho_boundary_analysis SEM across replicates + hollow floored markers + de-hardcoded ell_mean (measured from the run's graph); appendix_fluct per-N sigma + ~18x title (figB2); bootstrap_dynamics driving estimate so fig1 epoch-0 matches genesis. - pytest: 186 passed; report links 528/0 dangling. Co-Authored-By: Claude Opus 4.8 (1M context) --- reports/tsi/README.md | 4 +- reports/tsi/report-figures/fig1_bootstrap.png | Bin 251709 -> 241593 bytes .../report-figures/fig26_deficit_vs_rho.png | Bin 280599 -> 289155 bytes .../figB2_fluctuation_stats.png | Bin 247927 -> 248670 bytes ...i-report-1-overview-and-recommendations.md | 71 +++++++------- .../tsi/tsi-report-2-accuracy-and-design.md | 64 +++++++------ .../tsi-report-3-robustness-and-incentives.md | 74 +++++++++------ ...report-4-reproducibility-and-appendices.md | 88 +++++++++--------- .../tsi-sim-pernode/scripts/appendix_fluct.py | 7 +- .../scripts/bootstrap_dynamics.py | 6 +- .../scripts/rho_boundary_analysis.py | 54 +++++++++-- .../tsi-sim-pernode/scripts/stake_vs_delay.py | 6 +- .../tsi/tsi-sim-pernode/src/tsi_sim/config.py | 18 ++-- .../tsi-sim-pernode/src/tsi_sim/measure.py | 6 +- .../tsi-sim-pernode/src/tsi_sim/metrics.py | 22 +---- .../src/tsi_sim/plotting/figures_pernode.py | 11 ++- .../tsi/tsi-sim-pernode/src/tsi_sim/reorg.py | 7 +- .../tsi/tsi-sim-pernode/src/tsi_sim/theory.py | 14 +-- 18 files changed, 262 insertions(+), 190 deletions(-) diff --git a/reports/tsi/README.md b/reports/tsi/README.md index 9587fc6..26f115b 100644 --- a/reports/tsi/README.md +++ b/reports/tsi/README.md @@ -7,13 +7,13 @@ This report selects and justifies the TSI parameters for Cryptarchia from a per- ## Parts 1. **[Overview and recommendations](tsi-report-1-overview-and-recommendations.md)** — the executive summary, the per-knob parameter reference (§7), and the safest selection with residual risks and the recommendation-vs-spec deltas (§8). -2. **[Accuracy and design](tsi-report-2-accuracy-and-design.md)** — the model and counting rule (§2), the seven findings and their evidence (§3), and the design equations / selection algorithm (§4–§5). +2. **[Accuracy and design](tsi-report-2-accuracy-and-design.md)** — the model and counting rule (§2), the seven findings and their evidence (§3), the design equations and selection algorithm (§4), and the caveats and regime of validity (§5). 3. **[Robustness and incentives](tsi-report-3-robustness-and-incentives.md)** — jitter, grinding, withholding, selfish mining, the reward design, fork/reorg depth, and organic churn (§6). 4. **[Reproducibility and appendices](tsi-report-4-reproducibility-and-appendices.md)** — how to re-run every study (§9), the residual f-rounding offset (App A), the per-epoch noise floor (App B), and consensus detail (App C). ## Headline recommendation -Cryptarchia baseline f = 1/30: security `k = 2160`, uncle window `W = 300` slots, uncle cap `U = ⌈ρ⌉ + 1` (2 at the Blend target), learning rate `β = 1`, peering degree ≥ 6 at scale, soft uncle rewards with `w_u + w_n < 1`, and operate at load `ρ = f·D_vis < 1`. The full recommended-configuration table and rationale are in **[Part 1 →](tsi-report-1-overview-and-recommendations.md)**. +Cryptarchia baseline f = 1/30. Two design choices are foundational: count uncles **per occupied slot**, not per block — the density-bug fix that lands the estimate at exactly `D` ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§8.5](tsi-report-1-overview-and-recommendations.md#s8-5)) — and make genesis `D̂` **a single protocol constant, identical at every node**, never client-configurable, since a per-node divergence is never self-corrected ([§8.1](tsi-report-1-overview-and-recommendations.md#s8-1) row 7). The settings: security `k = 2160`, uncle window `W = 300` slots, uncle cap `U ≥ ⌈ρ⌉ + 1` (2 at the Blend target; the protocol's `MAX_UNCLES = 4` sits safely above it), learning rate `β = 1`, on-chain `f` at 10⁻⁶ precision, peering degree ≥ 6 at scale, soft uncle rewards with `w_u + w_n < 1`, and operate at load `ρ = f·D_vis < 1`. The full recommended-configuration table and rationale are in **[Part 1 →](tsi-report-1-overview-and-recommendations.md)**. ## Figures diff --git a/reports/tsi/report-figures/fig1_bootstrap.png b/reports/tsi/report-figures/fig1_bootstrap.png index c6f1a307b71707deec6596f4547a2a0c333633e3..c9d081bc171f99c969b505c2f7260abbe518f556 100644 GIT binary patch literal 241593 zcmeFZ_g7Qv7Bw6ZumZLtB2p9;l`2&_DxgSHks6vxZ=sh^6%`eb-lR$IAiaZ#)X;lJ zq=W#W_fXyyJ@?*o-tqnc-w$8La2S%EWbdb}HP@VT?GKOTA5a{>cpQO1P)I+Nc#1$A zQ$!%hyN;5>D^oF74d6dP8%b3gMU=jc{c|flgxqr*3saPhsnH8YJ3T9FBa}He`|aE8 zoUDw7HZ~U4f*c%X|2={oWo5t-T%U-7Z#ic1P|X^FU}qx!JLHfkW`{V0KuAm6edZ83 zKSCDvOmFDhvXh4%Zh_q>LGhlr`rRLhbI!qiBqvXPJI{LVtP8#lA^H7FVp(EYnbY%^ zm2;x5-17K^=K1dM?Sm{6ownu=2Cb2+k)<(&4>_u==i$r$_i(>KO*>2SzrW#`_#MVD z;${EuaWv^)N4UHBh5!EtAQ1oG90!T3(FHJdekDOc=hTYKqjvW;$E;?%Z`JH1^=h01HX%jmLn!s9yF%bOnq|1>)0?5j6v(VlNI`XhQ~XgV zd(^_#m@6T3ey{+;H=HO#Z8ThL`3>`7jZVKw1HI=@vq8H+{Wa>FcJYxz 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zJ($%3%_%0(r-Pkh@^X=`eBe*GV8+gQuSo4eQDGTADKV>GQaK}ZduiqoeEB$#>whS^l+9WrY6w0WIdt0Rkl5d1EAe7!v^B8je-473+CocTqw zv*nD1Iy5WRv41zXux|bUQHx#g&lJAM`|Nyy;U^@he7x4}&z-!hp9snwu{3>P6c+0y#mmlTK+@HLy3@HI+)qf1^?X_M}ki9kuI z&h|@Op>**sX2}a@E&Y4{|7-sGhx~7Sn+@#x#T6R|qwghnulWkS;~^V+Yrf@)sQ&=S CjAqmT diff --git a/reports/tsi/tsi-report-1-overview-and-recommendations.md b/reports/tsi/tsi-report-1-overview-and-recommendations.md index f258d8a..a38fdb6 100644 --- a/reports/tsi/tsi-report-1-overview-and-recommendations.md +++ b/reports/tsi/tsi-report-1-overview-and-recommendations.md @@ -18,7 +18,7 @@ **What we found** 1. **All nodes always agree.** In every run, at every network size and block rate tested (1 000–10 000 nodes at the production security parameter; to 32 000 in the size-scaling study, [§3.7](tsi-report-2-accuracy-and-design.md#s3-7); blocks every 10–30 s), all nodes computed *exactly* the same estimate — even though they constantly disagree about the newest blocks. The reason is structural: TSI measures a window buried deep in the finalized past, where every honest node sees identical history ([§3.1](tsi-report-2-accuracy-and-design.md#s3-1)). Two caveats keep this honest: agreement is not accuracy — nodes can unanimously agree on a wrong value (see next point) — and agreement is inherited from the common genesis value, not rebuilt: TSI maintains agreement but cannot repair a divergence that somehow arose ([Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC)). -2. **Network delay makes the estimate too low; uncle references fix it.** When blocks race, the losers ("orphans") drop off the chain and out of the count, so the network under-counts its own stake — by roughly a quarter to a third under Blend (the mix-network transport) delays, deepening with network size. Letting each block also reference recent orphans ("uncles") puts them back into the count — counting *slots*, so a slot with two winners still counts once — and a single uncle reference per block restores the estimate to **exactly the true stake** (the recommended cap adds a one-uncle margin, [§8](#s8)) (the only residual is an optional ~1 % from on-chain rounding of the target rate, [§2.2](tsi-report-2-accuracy-and-design.md#s2-2)/[Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA)) ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)). +2. **Network delay makes the estimate too low; uncle references fix it.** When blocks race, the losers ("orphans") drop off the chain and out of the count, so the network under-counts its own stake — by roughly a quarter to a third under Blend (the mix-network transport) delays, deepening with network size. The error is strictly one-sided: the equilibrium estimate is **bounded above by the true stake** — `D̂/D` cannot exceed 1 (no tested cell sits above 1 beyond sampling noise, which is why the accuracy plots are capped at 1; [§2.2](tsi-report-2-accuracy-and-design.md#s2-2)), so delay can only deflate the estimate, never inflate it. Letting each block also reference recent orphans ("uncles") puts them back into the count — counting *slots*, so a slot with two winners still counts once — and a single uncle reference per block restores the estimate to **exactly the true stake** (the recommended cap adds a one-uncle margin, [§8](#s8)) (the only residual is an optional ~1 % from on-chain rounding of the target rate, [§2.2](tsi-report-2-accuracy-and-design.md#s2-2)/[Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA)) ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)). 3. **Two sizing rules cover the deployments tested.** How many uncle slots a block needs (`U`) is dictated by the **load** — the number of blocks the whole network produces during the time one block needs to reach everyone (written `ρ`; formally `ρ = f·D_vis`, [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)). The load counts the concurrent blocks each new block must be able to reference, and one uncle slot drains one of them per block — so `U` must be at least the load rounded up, plus one spare. How far back a block may reach for an orphan (`W`) is dictated by block spacing, not delay: about ten block intervals. The formal equations, their calibration, and worked examples are in [§4](tsi-report-2-accuracy-and-design.md#s4). 4. **Cheating doesn't pay.** Hiding blocks to deflate the estimate costs the attacker more than anyone else, heals within one epoch, and — for a full withdrawal — the lower estimate is simply the *correct* count of who is still participating ([§6.4](tsi-report-3-robustness-and-incentives.md#s6-4)–[§6.5](tsi-report-3-robustness-and-incentives.md#s6-5)). The one genuinely profitable attack is classic selfish mining, which needs roughly one-third of all stake and afflicts every Nakamoto-style chain, not TSI specifically; the damage it does to the estimate is repaired by the same uncle mechanism ([§6.6](tsi-report-3-robustness-and-incentives.md#s6-6)). Rewarding uncles compensates the honest victims of delay and makes hiding strictly worse — but the reward must remain a bonus (a *soft* rule, never a validity requirement, which an attacker could turn into a tool for censoring or forking the chain), and the uncle + nephew rewards (the nephew reward pays the block that *includes* the reference) must together stay below one block reward, or deliberately orphaning one's own blocks becomes a business ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)). 5. **Reorganisations stay shallow if the load stays low.** Forks are the cost centre: a deep reorg discards confirmed blocks. Fork depth grows with delay, and uncles keep it shallow (without them the deflated estimate over-produces blocks, and honest reorgs reach ~17 deep; with them, ~4). Against a private-chain attacker holding 10–30 % of stake trying to force the deepest reorg, keeping the load below one (few honest forks) keeps reorgs bounded and shallow (single digits to low tens of blocks even at 30 % stake) — but past that, at 30 % stake and heavy delay, fork-induced orphaning tips the attacker over an effective majority and reorgs become unbounded. The same "keep `ρ < 1`" rule that keeps the estimate accurate keeps reorgs shallow ([§6.10](tsi-report-3-robustness-and-incentives.md#s6-10)). @@ -36,7 +36,7 @@ | TSI learning rate `β` | **1** (one-epoch tracking) | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) | | operating point | keep the **load below one** block per propagation delay, with margin | [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2), [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3) | | peering degree | **4 is fine for smaller networks (up to N ≈ 2×10⁵); ≥ 6 beyond** — degree 4 exhausts U = 1 near N ≈ 8×10⁵ | [§3.7](tsi-report-2-accuracy-and-design.md#s3-7), [§8](#s8) | -| uncle rewards | **soft** inclusion (never validity); substantial `w_u` with **`w_u + w_n < 1`** | [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) | +| uncle rewards | **soft** inclusion (never validity); substantial `w_u` (the uncle *reward*; not the spec's `w_u`, which is the uncle *window* — this report writes that `W`) with **`w_u + w_n < 1`** | [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) | *"Load" (`ρ`) in this table is the quantity defined in finding 3 above: blocks produced network-wide per block-propagation delay, `ρ = f·D_vis` ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)). Keeping it below one means a single uncle slot per block can absorb every concurrent block; the `+1` in the uncle cap is the safety margin.* @@ -48,7 +48,7 @@ This report is split into four parts (see the [index](README.md)): **Part 1** ## 7. Parameter reference — what each knob does -Every parameter a protocol designer or operator can set, in three groups: **protocol parameters** (design choices this report selects), **network/environment parameters** (given by the deployment; their impact must be measured and fed into the [§4](tsi-report-2-accuracy-and-design.md#s4) algorithm), and **model/attack knobs** (used to probe robustness). Each impact statement cites the section and figure that measured it; [§8](#s8) turns this reference into the recommended selection. +Every parameter a protocol designer or operator can set, in three groups: **protocol parameters** (design choices this report selects), **network/environment parameters** (given by the deployment; their impact must be measured and fed into the [§4](tsi-report-2-accuracy-and-design.md#s4) algorithm), and **model/attack knobs** (used to probe robustness). Each impact statement cites the section and figure that measured it; [§8](#s8) turns this reference into the recommended selection. Figure identifiers (`figN`) refer to figures embedded in the other parts, captioned **Fig N** there: `fig1`–`fig6`, `fig16`, `fig19`, `fig20`, `fig22`–`fig26` in [Part 2](tsi-report-2-accuracy-and-design.md); `fig7`–`fig15`, `fig27`–`fig29` in [Part 3](tsi-report-3-robustness-and-incentives.md); `fig17`, `fig18`, `fig21`, `figB1`, `figB2` in [Part 4](tsi-report-4-reproducibility-and-appendices.md). ### 7.1 Protocol parameters @@ -56,11 +56,11 @@ Every parameter a protocol designer or operator can set, in three groups: **prot | parameter | controls | measured impact | where | |---|---|---|---| | `f` — block rate (1/30) | block interval `1/f`; scales every threshold | recovery stays at 1.0 at every rate (slot-counting removes the `c(f)` dependence); `U_min ∝ f` (an 8-s delay needs U = 1 at 30/20-s blocks but U = 2 at 15/10-s); `W_min ∝ 1/f` (constant ≈ 7 block intervals); consensus-safety f-independent | [§3.6](tsi-report-2-accuracy-and-design.md#s3-6), fig6 | -| `k` — security parameter (2160) | finality depth **and** the slot geometry: epoch length `10·⌊k/f⌋`, TSI window `T = 6·⌊k/f⌋` slots | the density window sits a full epoch past k-finality — the structural reason tip churn (fig18) and jitter ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)) never reach the estimate; agreement confirmed at k = 2160; robustness studies at scaled k = 256 shrink `T` proportionally but leave the density-*ratio* mechanics unchanged | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1) fig17; [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1) | -| `U` — uncle cap (`max_uncles`) | orphan-recovery capacity per block | U = 0 biased low (0.64–0.74, worsens with N); `U ≥ ⌈ρ⌉` hard bound — below it *no* window recovers; `⌈ρ⌉ + 1` recommended; also the adversarial safeguard ([§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)) and the selfish-deflation repair ([§6.6](tsi-report-3-robustness-and-incentives.md#s6-6)) | [§3.2](tsi-report-2-accuracy-and-design.md#s3-2)/3.3/3.5, figs 2, 16, 20 | +| `k` — security parameter (2160) | finality depth **and** the slot geometry: epoch length `10·⌊k/f⌋`, TSI window `T = 6·⌊k/f⌋` slots | the density window opens a full epoch back and closes `4·⌊k/f⌋` slots (≈ 4k blocks) before the estimate is used — well past k-finality — the structural reason tip churn (fig18) and jitter ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)) never reach the estimate; agreement confirmed at k = 2160; robustness studies at scaled k = 256 shrink `T` proportionally but leave the density-*ratio* mechanics unchanged | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1); [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (figs 17, 18); [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1) | +| `U` — uncle cap (`max_uncles`) | orphan-recovery capacity per block | U = 0 biased low (0.64–0.74, worsens with N); `U ≥ ⌈ρ⌉` hard bound — below it *no* window recovers; `⌈ρ⌉ + 1` recommended; also the adversarial safeguard ([§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)) and the selfish-deflation repair ([§6.6](tsi-report-3-robustness-and-incentives.md#s6-6)) | [§3.2](tsi-report-2-accuracy-and-design.md#s3-2)/3.3/3.5, figs 2, 16, 20, 26 | | `W` — uncle window (`uncle_window` = 300) | how old an orphan may be and still be referenced | hard floor `≈ 7/f`, set by block *spacing* (FIFO queueing), not delay; no U buys below it; a generous W also keeps the emergent reference rate `p_ref` high, which the reward design relies on | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4)/3.5, figs 4, 5, 22; [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) fig15 | -| `β` — TSI learning rate (`BETA_DEFAULT` = 1) | estimator responsiveness: `D̂` is an EMA of active stake, `τ = −1/ln(1−β)` epochs | β = 1 tracks with a one-epoch lag (erases a withhold notch in one epoch); slower β shrinks the notch amplitude (0.35 → 0.15 for β 1 → 0.25) but leaves attacker profitability unchanged | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5)(i)–(iii), figs 10–12 | -| `uncle_strategy` (oldest) | which queued orphans a block references | all results use oldest-first (FIFO) — the drain model behind the `W ≈ 7/f` floor; the spec's unbiased coin (`uncle_random_p = 0.5`) was not swept (untested sensitivity, covered by the `W = 10/f` margin) | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | +| `β` — TSI learning rate (`BETA_DEFAULT` = 1) | estimator responsiveness: `D̂` is an EMA of active stake, `τ = −1/ln(1−β)` epochs | β = 1 tracks with a one-epoch lag (erases a withhold notch in one epoch); slower β shrinks the notch amplitude (0.35 → 0.13 for β 1 → 0.25) but leaves attacker profitability unchanged | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5)(i)–(iii), figs 10–12 | +| `uncle_strategy` (oldest) | which queued orphans a block references | all results use oldest-first (FIFO) — the drain model behind the `W ≈ 7/f` floor; a random draw among the queued orphans would drain one no faster, so the `W = 10/f` margin covers that alternative | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | | `w_u`, `w_n` — uncle / nephew rewards | compensation for referenced orphans / for referencing them | fairness: honest recovery 0.61 → 1.00 as `w_u` 0 → 1 (at `p_ref` = 1); hiding forfeits both rewards; safety invariant **`w_u + w_n < 1`** (else uncle farming pays); raising `w_n` alone marginally *helps* the attacker | [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)/6.8, figs 14, 15 | | inclusion rule | whether references are incentivised or mandated | **soft** (reward-weighted) only — a hard validity mandate cannot be encoded fork-safely (censorship or consensus fork) | [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) | | `genesis_d_factor`, `init_dest` | the initial `D̂` | a *common* wrong guess self-corrects in ~2 epochs (fig1); a *heterogeneous* init is preserved forever (fig21) — genesis `D̂` must be a shared constant | [§3.2](tsi-report-2-accuracy-and-design.md#s3-2), [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) | @@ -71,13 +71,13 @@ Every parameter a protocol designer or operator can set, in three groups: **prot | parameter | controls | measured impact | where | |---|---|---|---| -| `n_nodes` N | network size | consensus exact at every N (1 000–32 000 direct, fig17/fig23); U = 0 under-count deepens with N (0.739 → 0.635); `U`/`W` *thresholds* ≈ N-invariant at fixed delay — but at a fixed blending budget N raises the load through `ℓ_mean ∝ ln N`, exhausting U = 1 on a degree-4 graph near N ≈ 8×10⁵ ([§3.7](tsi-report-2-accuracy-and-design.md#s3-7)) | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1)/3.2/3.4/3.7, figs 2, 17, 20, 23, 24 | +| `n_nodes` N | network size | consensus exact at every N (1 000–32 000 direct, fig17/fig23); U = 0 under-count deepens with N (0.739 → 0.635); `U`/`W` *thresholds* ≈ N-invariant at fixed delay — but at a fixed blending budget N raises the load through `ℓ_mean ∝ ln N`, exhausting U = 1 on a degree-4 graph near N ≈ 8×10⁵ ([§3.7](tsi-report-2-accuracy-and-design.md#s3-7)) | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1)/3.2/3.4/3.7, figs 2, 20, 23, 24; [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (fig17) | | `topology` | propagation model | `blend` (**primary**): whole-second hops — the regime where `U`/`W` matter; `regular` (direct gossip, contrast): sub-slot links, `ρ ≈ 0.04`, U = 0 near-exact; `full_mesh`: reduced-model bridge, cross-validation only | [§2](tsi-report-2-accuracy-and-design.md#s2), [§3.3](tsi-report-2-accuracy-and-design.md#s3-3), figs 3, 16, 19 | -| `degree` | peering density | deg 6 vs 4: tip agreement 0.993–0.994 vs 0.988–0.989; U = 0 accuracy ≈ 1.00 vs ≈ 0.98 at 0.2-slot links; sets the diameter slope `ℓ_mean ≈ a_d·ln N` (`a₄`/`a₆`/`a₈` = 0.33/0.19/0.14) — one degree step (4 → 6) buys ~5 000× larger N at the same blending budget | figs 18, 19, 23, 24; [§3.7](tsi-report-2-accuracy-and-design.md#s3-7), [§4](tsi-report-2-accuracy-and-design.md#s4) | -| `link_latency_mean`, `link_latency_dist` | per-link transport latency (mean, shape) | sub-slot links: forks negligible; near a full slot: U = 0 dips to 0.84–0.91; the design law uses only the *mean* (`D_vis`) — confirmed by the exp-vs-geo comparison at equal mean (U ≥ 1 identical; only the U = 0 depth moves, ≤ 0.07) | [§2](tsi-report-2-accuracy-and-design.md#s2), [§3.3](tsi-report-2-accuracy-and-design.md#s3-3), fig19 | -| `blend_hops`, `blend_delay_max` | Blend-cascade length, per-hop delay bound | dominant `D_vis` term `hops·δ_max/2`; more hops at fixed budget degrade U = 1 exactly as the load predicts (0.98 → 0.48 across hops 3 → 6 at delay 16) | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3), figs 3, 16 | -| `jitter_mean`, `jitter_dist`, `jitter_frac` | stochastic per-(block,node) arrival jitter (Exp, or Poisson long-tail hitting a fraction of deliveries) | consensus and accuracy untouched up to 3 slots of Exp jitter (200/200 cells); the 10 % Poisson(3) long-tail model shifts U = 1 accuracy < 1 % per cell (~0.4 % mean, ~0.03 % pooled, within replicate SEM) and consensus not at all (378/378 cells); only tip agreement degrades (≈ 0.99 → 0.95) | [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1), [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) | -| `stake_dist` (`pareto_shape`, `total_stake`) | per-node stake weights | consensus identical under uniform, Pareto 1.16, and Pareto 1.33; U ≥ 1 accuracy indistinguishable across all three; only the U = 0 under-count moves with concentration (heavier tail → shallower: 0.815 Pareto vs 0.785 uniform; 1.33 ≈ 0.04 deeper than 1.16); whale-coalition reward statistics untested | [§2](tsi-report-2-accuracy-and-design.md#s2), [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) scope | +| `degree` | peering density | deg 6 vs 4: tip agreement 0.985–0.993 vs 0.988–0.994; U = 0 accuracy ≈ 1.00 vs ≈ 0.99 at 0.2-slot links; sets the diameter slope `ℓ_mean ≈ a_d·ln N` (`a₄`/`a₆`/`a₈` = 0.33/0.19/0.14) — one degree step (4 → 6) buys ~5 000× larger N at the same blending budget | figs 19, 23, 24; [§3.7](tsi-report-2-accuracy-and-design.md#s3-7), [§4](tsi-report-2-accuracy-and-design.md#s4); [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (fig18) | +| `link_latency_mean`, `link_latency_dist` | per-link transport latency (mean, shape) | sub-slot links: forks negligible; near a full slot: U = 0 dips to 0.88–0.93; the design law uses only the *mean* (`D_vis`) — confirmed by the exp-vs-geo comparison at equal mean (U ≥ 1 identical; only the U = 0 depth moves, ≤ 0.09) | [§2](tsi-report-2-accuracy-and-design.md#s2), [§3.3](tsi-report-2-accuracy-and-design.md#s3-3), fig19 | +| `blend_hops`, `blend_delay_max` | Blend-cascade length, per-hop delay bound | dominant `D_vis` term `hops·δ_max/2`; more hops at fixed budget degrade U = 1 exactly as the load predicts (0.96 → 0.51 across hops 3 → 6 at `δ_max` = 16 s, N = 1 000) | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3), figs 3, 16 | +| `jitter_mean`, `jitter_dist`, `jitter_frac` | stochastic per-(block,node) arrival jitter (Exp, or Poisson long-tail hitting a fraction of deliveries) | consensus and accuracy untouched up to 3 slots of Exp jitter (200/200 runs); the 10 % Poisson(3) long-tail model shifts U = 1 accuracy by ~0.4 % per cell on average (~0.03 % pooled; up to ~1.5 % in the noisiest large-N cell — N = 16 000, degree 8, δ_max = 4 s, ≈ 2× that cell's replicate SEM) and consensus not at all (378/378 cells); only tip agreement degrades (≈ 0.99 → 0.95) | [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1), [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) | +| `stake_dist` (`pareto_shape`, `total_stake`) | per-node stake weights | consensus identical under uniform, Pareto 1.16, and Pareto 1.33; U ≥ 1 accuracy indistinguishable across all three; only the U = 0 under-count moves with concentration (heavier tail → shallower: 0.815 Pareto vs 0.785 uniform; 1.33 at most ≈ 0.025 deeper than 1.16, mean 0.012 over the four matched cells, each within ≈ 1.5 SEM); whale-coalition reward statistics untested | [§2](tsi-report-2-accuracy-and-design.md#s2), [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) scope | ### 7.3 Model and attack knobs (robustness probes) @@ -86,7 +86,7 @@ Every parameter a protocol designer or operator can set, in three groups: **prot |---|---|---|---| | `adversary_frac` (β_adv), `adversary_strategy` | uncle suppression / abstention withholding | suppression weak at ρ < 1, a cheap lever only at ρ > 1 (1.43× at ρ = 1.36, β_adv = 0.5); withholding → `D̂ ≈ (1−β_adv)` — the *correct* active-stake answer, topology-independent | [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)/6.4, figs 8, 9 | | `adversary_period`, `adversary_withhold_epochs` | dynamic withhold-rejoin schedules | unprofitable at every duty ψ > 0; griefing bounded (`deflation = β_adv·ψ`); no persistence | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5), figs 10–12 | -| private-chain reorg (α = 0/10/20/30 %) | deepest-reorg longest-chain attack | reorg-depth tail `(α_eff/(1−α_eff))^d` with `α_eff=α/(α+(1−α)(1−o))`; shallow at ρ<1, unbounded at 30 % once forks push `α_eff>½` | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10), figs 27, 28 | +| private-chain reorg (`α` = 0/10/20/30 %) | deepest-reorg longest-chain attack | `α` = the attacking coalition's stake fraction — the selfish-mining notation for `β_adv` above, and distinct from the TSI learning rate `β` ([§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)); reorg-depth tail `(α_eff/(1−α_eff))^d` with the *effective* share `α_eff=α/(α+(1−α)(1−o))` (`o` = honest fork rate); shallow at ρ<1, unbounded at 30 % once forks push `α_eff>½` | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10), figs 27, 28 | | `fork_rate`, `max_reorg_depth` (engine outputs) | measured fork structure | honest fork rate 0.2→0.6 over δ=2→32 s; max reorg depth 2→4 (U=2), up to 17 at U=0 | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10), fig28 | | `α`, `γ` (selfish race) | private-chain withholding | profitable above `(1−γ)/(3−2γ)` (⅓ at γ = 0); the optimal MDP barely beats SM1 at γ = 0 | [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6), figs 13, 14 | | `η` — uncle-recovery fraction | estimator repair under selfish orphaning | `D̂` 0.70 → 0.82 → 0.94 as η 0 → 0.5 → 1 (α = 0.4) | [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6), fig13 | @@ -99,39 +99,39 @@ Every parameter a protocol designer or operator can set, in three groups: **prot ## 8. Safest parameter selection and design -Everything below is assembled from this report's own measurements; each row cites the section and figure that justifies it. This is the authoritative selection — [§1](#s1)'s table is its preview. +Everything below is assembled from this report's own measurements; each row cites the section and figure that justifies it. This is the authoritative selection — [§1](#s1)'s table is its preview. Figure identifiers follow the [§7](#s7) key. ### 8.1 The selection | # | parameter / decision | safest choice | why (this report's finding) | evidence | |---|---|---|---|---| -| 1 | security `k` | **2160** (finality-driven) | per-node spread ≡ 0 and window agreement ≡ 1.000 at k = 2160 for all N = 1 000–10 000 and f = 1/10–1/30; the mechanism (window buried past k-finality) is k-independent; k = 2160 is tested at full scale, and the [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) ladder confirms the same exact agreement at the scaled k = 256 up to N = 32 000 | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1), figs 17, 18 | +| 1 | security `k` | **2160** (finality-driven) | per-node spread ≡ 0 and window agreement ≡ 1.000 at k = 2160 for all N = 1 000–10 000 and f = 1/10–1/30; the mechanism (window buried past k-finality) is k-independent; k = 2160 is tested at full scale, and the [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) ladder confirms the same exact agreement at the scaled k = 256 up to N = 32 000 | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1); [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (figs 17, 18) | | 2 | block rate `f` | **1/30** (given) — treat as a coupled input | `f` moves every threshold: `U_min ∝ f`, `W_min ∝ 1/f` (recovery stays at 1.0 at all rates); re-derive `U`, `W`, `ρ` if `f` ever changes | [§3.6](tsi-report-2-accuracy-and-design.md#s3-6), fig6 | -| 3 | uncle window `W` | **300 slots = 10/f**; widen to **450–600 (15–20/f)** when operating near the load boundary `ρ ≈ 1` | hard floor ≈ 7/f set by block spacing (N-invariant, fig25); below it no uncle count recovers (delay 16, W = 100: even U = 4 only 0.94); `W` is the buffer for block-production *fluctuations* — at `ρ ≈ 1`, W = 600 recovers what W = 300 loses (fig25), a cheap alternative to the `+1` uncle; the 10/f margin also covers the untested spec coin-rule sensitivity ([§3.4](tsi-report-2-accuracy-and-design.md#s3-4)) and keeps the emergent reference rate `p_ref` ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)) high for the reward design | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4)/3.5, figs 4, 5, 22, 25; [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) | -| 4 | uncle cap `U` | **`⌈ρ⌉ + 1`** (Blend, the deployment target); **1** suffices for plain direct gossip (ρ ≈ 0.04) | `U < ρ` never recovers; `⌈ρ⌉` is tight but under-shoots just below integer ρ — at ρ = 0.96, U = 1 fails at 0.962 ± 0.006 (3σ below the 0.98 bar): the direct evidence for the +1 margin; one uncle lifts every tested delay to full recovery (≈ 1.0) at N = 10 000 | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)/3.5/3.6, figs 6, 16, 20 | -| 5 | TSI learning rate `β` | **1** (`BETA_DEFAULT`) | one-epoch tracking of active stake: any withhold notch is erased in one epoch; attacker profitability is β-independent, so slowing β buys the defender nothing. *Disclosure:* the one regime where distortion per unit of network reward forfeited exceeds 1 (bounded ≤ 2×) is β ≥ 1 with a ≈ 50 % coalition (rejoin overshoot) — a protocol-chosen gain, not an adversary lever | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5), figs 10–12 | +| 3 | uncle window `W` | **300 slots = 10/f**; widen to **450–600 (15–20/f)** when operating near the load boundary `ρ ≈ 1` | hard floor ≈ 7/f set by block spacing (N-invariant, fig25); below it no uncle count recovers (delay 16, W = 100: even U = 4 only 0.94); `W` is the buffer for block-production *fluctuations* — at `ρ ≈ 1`, W = 600 recovers what W = 300 loses (fig25), a cheap alternative to the `+1` uncle; the 10/f margin also covers the uncle-selection sensitivity (oldest-first vs a random draw; [§3.4](tsi-report-2-accuracy-and-design.md#s3-4)) and keeps the emergent reference rate `p_ref` ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)) high for the reward design | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4)/3.5, figs 4, 5, 22, 25; [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) | +| 4 | uncle cap `U` | **`⌈ρ⌉ + 1`** (Blend, the deployment target); **1** suffices for plain direct gossip (ρ ≈ 0.04) | `U < ρ` never recovers; `⌈ρ⌉` is tight but under-shoots just below integer ρ — at ρ = 0.96, U = 1 fails at 0.962 ± 0.006 (3σ below the 0.98 bar): the direct evidence for the +1 margin, corroborated by the dedicated 40-cell ρ-boundary sweep (U = 1 only ≈ 0.966 at ρ = 0.96, a 4σ shortfall, and already ≈ 0.976 at ρ = 0.91 — `⌈ρ⌉` under-shoots from ρ ≈ 0.9, fig26); one uncle lifts every tested delay to full recovery (≈ 1.0) at N = 10 000 | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)/3.5/3.6, figs 6, 16, 20, 26 | +| 5 | TSI learning rate `β` | **1** (`BETA_DEFAULT`) | one-epoch tracking of active stake: any withhold notch is erased in one epoch; attacker profitability is β-independent, so slowing β buys the defender nothing. *Disclosure:* the one regime where distortion per unit of network reward forfeited exceeds 1 (bounded ≤ 2×) is β ≥ 1 (rejoin overshoot, across the tested coalitions) — a protocol-chosen gain, not an adversary lever; and because `β = 1` tracks with a one-epoch (≈ 7.5-day) lag, `D̂` reflects participating stake from ~1–2 weeks ago and cannot resolve *sub-epoch* participation cycles (the estimator's Nyquist limit) — the correct trade for organic churn, detailed in [§6.11](tsi-report-3-robustness-and-incentives.md#s6-11) | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5), [§6.11](tsi-report-3-robustness-and-incentives.md#s6-11), figs 10–12 | | 6 | operating point | **`ρ = f·D_vis < 1` with margin** | the fitted static feedback map folds near ρ ≈ 1 (provisioning warning — the full dynamics never reach it); grinding is weak at ρ < 1 (1.04×) but cheap at ρ > 1 (1.43×); chronic ρ > 1 under-count persists after any attack ends. ρ < 1 is simultaneously the honest-accuracy and the adversarial safeguard | [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) fig7; [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3) fig8; [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5)(iv) fig12 | | 7 | genesis / initialization | **genesis `D̂` is a single protocol constant, identical at every node** — never client-configurable | consensus is an *initialization* property, not a restoring force: an injected per-node spread is conserved forever (max/min ≈ 3.0, flat), while a *common* wrong guess self-corrects in ~2 epochs | [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (fig21); [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) fig1 | -| 8 | uncle validity precondition | **a counted uncle must be a real VRF lottery winner for its slot, enforced on-chain** | fabrication is VRF-impossible; this precondition underlies every [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)–[§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) bound and caps uncle issuance at `≤ U·(w_u + w_n)` per block | [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3), [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)(a) | +| 8 | uncle validity precondition | **a counted uncle must be a real lottery winner for its slot — already enforced on-chain by the spec's ZK Proof-of-Leadership** | fabrication is cryptographically impossible (the ZK Proof-of-Leadership cannot be forged); this precondition underlies every [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)–[§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) bound and caps uncle issuance at `≤ U·(w_u + w_n)` per block | [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3), [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)(a) | | 9 | uncles in the density | **recovered uncles enter the TSI counted density** (independent of rewarding them) | restores `D̂` under honest latency (0.64–0.74 → 1.0) *and* under selfish orphaning (0.70 → 0.94 at η = 1) — a safety win with no reward-schedule dependence | [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) fig2; [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6) fig13 | | 10 | inclusion rule | **soft (reward-weighted) — never a validity rule** | a hard mandate cannot be encoded fork-safely: the objective encoding is a censorship weapon, the subjective one forks consensus with no adversary; under the soft rule `p_ref` is emergent and high — at `p_ref ≈ 0.85` the selfish share (0.420 at α = 0.4) is already below block-only (0.484) and near stake | [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) fig15 | -| 11 | reward schedule | **substantial `w_u` (Ethereum's GHOST-style uncle rewards are the precedent); `w_u + w_n < 1` strictly enforced** | farming a real VRF win into a self-uncle + self-nephew pays `w_u + w_n` against an honest block's 1 — the binding invariant is the *sum* (0.875 + 0.03125 = 0.906 is safe; 0.875 + 0.15 = 1.025 is not); `w_u` compensates honest orphans (recovery → 1.0) and makes hiding forfeit both rewards | [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)(a), figs 14, 15 | -| 12 | peering degree | **degree 4 is acceptable for smaller networks — up to N ≈ 2×10⁵ it keeps the load under 0.9 at the 8-s budget; use ≥ 6 beyond, and scale with the target size** | degree sets the gossip-diameter slope `ℓ_mean ≈ a_d·ln N`, and at a fixed blending budget that slope decides when `U = 1` runs out: at δ = 8 s, degree 4 exhausts U = 1 near **N* ≈ 8×10⁵** (its ladder curve already touches the recovery bar at N = 32 000), degree 6 holds to N ~ 4×10⁹, degree 8 to ≈ 6×10¹² — one degree step (4 → 6) buys ~5 000× more network at the same budget. Degree and the uncle cap are exchangeable defences against growth: densify the graph or add an uncle slot, whichever is cheaper. Plus the small-N benefits: tip agreement 0.993–0.994 vs 0.988–0.989, better U = 0 recovery | [§3.7](tsi-report-2-accuracy-and-design.md#s3-7), figs 23, 24; figs 18, 19 | +| 11 | reward schedule | **substantial `w_u` (Ethereum's GHOST-style uncle rewards are the precedent); `w_u + w_n < 1` strictly enforced** | farming a real leadership win into a self-uncle + self-nephew pays `w_u + w_n` against an honest block's 1 — the binding invariant is the *sum* (0.875 + 0.03125 = 0.906 is safe; 0.875 + 0.15 = 1.025 is not); `w_u` compensates honest orphans (recovery → 1.0) and makes hiding forfeit both rewards | [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)(a), figs 14, 15 | +| 12 | peering degree | **degree 4 is acceptable for smaller networks — up to N ≈ 2×10⁵ it keeps the load under 0.9 at the 8-s budget; use ≥ 6 beyond, and scale with the target size** | degree sets the gossip-diameter slope `ℓ_mean ≈ a_d·ln N`, and at a fixed blending budget that slope decides when `U = 1` runs out: at δ = 8 s, degree 4 exhausts U = 1 near **N* ≈ 8×10⁵** (its ladder curve already touches the recovery bar at N = 32 000), degree 6 holds to N ~ 4×10⁹, degree 8 to ≈ 6×10¹² — one degree step (4 → 6) buys ~5 000× more network at the same budget. Degree and the uncle cap are exchangeable defences against growth: densify the graph or add an uncle slot, whichever is cheaper. Plus the small-N benefit of better U = 0 recovery (tip agreement is comparable: deg 6 0.985–0.993 vs deg 4 0.988–0.994) | [§3.7](tsi-report-2-accuracy-and-design.md#s3-7), figs 23, 24; fig19; [Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC) (fig18) | | 13 | Blend delay budget | **choose `hops·δ_max` so `ρ ≲ 1`**; if `U ≥ ⌈ρ⌉` exceeds the uncle-slot budget, cut blending — no window fixes `U < ρ` | worked examples: 3 hops × 8 s at f = 1/30 → ρ ≈ 0.56, U = 2 recommended; the same Blend at f = 1/10 → ρ ≈ 1.7, U = 3 | [§4](tsi-report-2-accuracy-and-design.md#s4); [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3)(iii) | | 14 | on-chain `f` precision | **carry the target rate `f` at 10⁻⁶ precision** (was 10⁻³) | removes the sole residual bias after slot-counting — the ≈ 1 % `f/f_p` over-estimate (a ~1 % win-probability under-delivery and slow canonical pace); one-constant change, no dynamics cost, no fork risk. **Exceeded** in this report's estimator, which uses exact `f` (residual 0), finer than the recommended 10⁻⁶ bump (`f_p = 0.033333`, residual < 10⁻⁵) | [§2.2](tsi-report-2-accuracy-and-design.md#s2-2), [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA) | -| 15 | reorg / confirmation depth | keep **`ρ < 1`** so fork-induced amplification stays below the effective-majority cliff; for soft settlement, wait `d` blocks per the [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) tail (≈ 4/8/17 blocks for 99.9 % against 10/20/30 % stake) | reorg depth is bounded and shallow only while the honest fork rate is low; at 30 % stake past `ρ ≈ 1` it is unbounded ([§6.10](tsi-report-3-robustness-and-incentives.md#s6-10), figs 27–28) | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) | +| 15 | reorg / confirmation depth | keep **`ρ < 1`** so fork-induced amplification stays below the effective-majority cliff; for soft settlement, wait `d` blocks per the [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) tail (≈ 4/8/17 blocks for 99.9 % against 10/20/30 % stake at N = 1 000, degree 6 — deeper on larger or sparser networks, per the [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) scale table) | reorg depth is bounded and shallow only while the honest fork rate is low; at 30 % stake past `ρ ≈ 1` it is unbounded ([§6.10](tsi-report-3-robustness-and-incentives.md#s6-10), figs 27–28) | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) | ### 8.2 Design decisions and their rationale -**The levers are hierarchical, not fungible.** Size `W` first (10/f — the floor is set by block spacing and no uncle count buys below it), then `U` from the load `⌈ρ⌉ + 1`, then check the operating point `ρ < 1` (fig5, fig22: at delay 32, ρ ≈ 1.7, even the widest window recovers only 0.61 at U = 1). +**The levers are hierarchical, not fungible.** Size `W` first (10/f — the floor is set by block spacing and no uncle count buys below it), then `U` from the load `⌈ρ⌉ + 1`, then check the operating point `ρ < 1` ([§3.4](tsi-report-2-accuracy-and-design.md#s3-4)/[3.5](tsi-report-2-accuracy-and-design.md#s3-5), fig22, fig5: at delay 32, ρ ≈ 1.7, even the widest window recovers only 0.61 at U = 1). **One mechanism, three duties.** The same uncle references fix the honest latency under-count ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)), repair the estimator under uncle-suppression and selfish orphaning ([§6.3](tsi-report-3-robustness-and-incentives.md#s6-3), [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6)), and — rewarded softly — pay the fairness and anti-hiding incentives ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)). This is why the design invests in `W`/`U` margin rather than in any inclusion mandate: every marginal slot of window or uncle capacity strengthens all three duties at once. **Why soft, not hard, inclusion.** "Owed" cannot be proven — no node can prove which forks a producer saw. An objective slot-gap encoding lets an attacker withhold-then-late-release an uncle to retroactively invalidate honest blocks (censorship); a visibility encoding is subjective and forks consensus with no adversary at all ([§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)). The soft rule concedes only a small residual (quantified in [§8.3](#s8-3) item 3): a bounded near-threshold backfire that vanishes as the emergent `p_ref` rises, and a per-α premium that stays ≤ +0.014 even at full inclusion. -**What TSI defends, and what it measures.** Abstention-style withholding is strictly unprofitable (reward/stake 0.94 → 0.30 for duty 0.10 → 0.75 at β_adv = 0.3), bounded as griefing (deflation = β_adv·ψ), non-persistent, and does not stack across coalitions ([§6.5](tsi-report-3-robustness-and-incentives.md#s6-5), [§6.9](tsi-report-3-robustness-and-incentives.md#s6-9)) — and a full withdrawal is *correctly measured*, not mis-measured: `D̂ → (1−β_adv)` is the right answer for the participating stake ([§6.4](tsi-report-3-robustness-and-incentives.md#s6-4)). The one profitable lever is classic selfish mining above `(1−γ)/(3−2γ)` — a general Nakamoto-PoS result, not TSI-specific; TSI's added exposure (estimator deflation to 0.70 at α = 0.4) is repaired by uncle-counting (row 9), and the profit premium is blunted, not eliminated, by the soft-rewarded references (row 10). The adversary frontier is exactly optimal selfish mining; no compounding lever remains ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)). +**What TSI defends, and what it measures.** Abstention-style withholding is strictly unprofitable (reward/stake 0.95 → 0.31 for duty 0.10 → 0.75 at β_adv = 0.3), bounded as griefing (deflation = β_adv·ψ), non-persistent, and does not stack across coalitions ([§6.5](tsi-report-3-robustness-and-incentives.md#s6-5), [§6.9](tsi-report-3-robustness-and-incentives.md#s6-9)) — and a full withdrawal is *correctly measured*, not mis-measured: `D̂ → (1−β_adv)` is the right answer for the participating stake ([§6.4](tsi-report-3-robustness-and-incentives.md#s6-4)). The one profitable lever is classic selfish mining above `(1−γ)/(3−2γ)` — a general Nakamoto-PoS result, not TSI-specific; TSI's added exposure (estimator deflation to 0.70 at α = 0.4) is repaired by uncle-counting (row 9), and the profit premium is blunted, not eliminated, by the soft-rewarded references (row 10). The adversary frontier is exactly optimal selfish mining; no compounding lever remains ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)). ### 8.3 Residual risks and open items @@ -142,12 +142,15 @@ Everything below is assembled from this report's own measurements; each row cite 4. **No re-convergence ([Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC)).** Any mechanism that could inject persistent per-node `D̂` disagreement (genesis/clock exploit) would never be self-corrected — safety rests entirely on row 7. 5. **Adversarial `U` margin unquantified ([§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)).** Under attack-inflated orphaning (orphan/blocks ≈ 0.35 at α = 0.46) the honest-load cap may need extra margin (owed uncles beyond `U` defer and can age out of `W`); this report does not size it. 6. **Clock skew — bounded, not a break ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)).** A per-node whole-timeline slot-clock shift moves each node's window bounds, giving a bounded inter-node spread `≤ 2·skew/T` (`< 10⁻⁴` at the production window). Small and quantified, but — unlike per-arrival jitter — not identically zero; large skew is still an untested extreme. -7. **Semi-empirical constants ([§5](tsi-report-2-accuracy-and-design.md#s5)).** `a = 2.01` and the 7/f floor are fits; eq 4′ is an N ≈ 1 000 fit that worsens with N — for production sizing use the margined rules (rows 3–4) and the fully-recovered accuracy 1.0, never eq 4′. +7. **Semi-empirical constants ([§5](tsi-report-2-accuracy-and-design.md#s5)).** `a ≈ 2` and the 7/f floor are fits; eq 4′ is an N ≈ 1 000 fit that worsens with N — for production sizing use the margined rules (rows 3–4) and the fully-recovered accuracy 1.0, never eq 4′. 8. **Residual ~1 % offset — resolved here, pending in the spec ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2), row 14, [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA)).** After the slot-counting fix the only systematic offset is the 10⁻³ rounding of `f` (≈ 1 % `f/f_p` over-estimate); this report's estimator applies the row-14 precision bump, but the **spec still uses 10⁻³** and should adopt it. 9. **Multi-coalition reorg — bounded, but worse than a single coalition ([§6.9](tsi-report-3-robustness-and-incentives.md#s6-9), [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10)).** The [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) tail is single-coalition. For `K` competing private-chain coalitions with total stake `α_tot`, the deepest reorg any one coalition (stake `α_i`) can drive against the public chain is bounded by `α_eff,i = α_i / (α_i + (1−α_tot)(1−o′))`, where `o′` is the public fork rate *inflated by every coalition's released-block orphaning*. Two channels make competition **worse** than a single colluding `α_tot` coalition: the rival coalitions' stake leaves the public chain (the honest term carries `(1−α_tot)`, not `(1−α_i)`), and their mutual orphaning lifts `o′` above the honest baseline `o` — in the limit `o′→1` even a sub-majority coalition faces a stalled public chain and reorgs unboundedly. So the single-coalition tail is best-case-for-the-defender; the safe design response is the same rule as everywhere else — size against `α_tot`, and keep `ρ < 1` so the honest baseline `o` stays small and caps how far mutual orphaning can inflate `o′`. 10. **Soft-rule bribery is cheap per block ([§6.9](tsi-report-3-robustness-and-incentives.md#s6-9)).** A bribe > `w_n` buys one block's omitted references — bounded in effect (other honest blocks in `W` still reference), but the hard-mandate defence is unavailable *by design*. -11. **Untested adversary variants ([§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) scope).** Pareto whale coalitions, very slow `β`, jitter > 0 for the dynamic-withhold results, and the spec's coin-flip uncle selection; the reported bounds are best-case-for-the-defender (the adaptive-schedule case is closed in [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)). -12. **Network partition/heal — reasoned, not simulated ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)).** TSI reads its density window a full epoch (`E` slots) past `k`-finality, so a partition that heals *within* the finality depth is invisible: all honest nodes reconverge on one canonical chain before the measurement window closes and compute an identical `D̂` — the same finality-window argument that makes jitter and clock skew harmless ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)). A partition lasting *longer* than finality is a consensus-layer safety failure (the chain forks irreparably) that TSI inherits but does not worsen — it adds no partition vulnerability of its own. A direct partition-and-heal simulation is left as future work. +11. **Untested adversary variants ([§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) scope).** Pareto whale coalitions, very slow `β`, jitter > 0 for the dynamic-withhold results, and a random (rather than oldest-first) uncle-selection draw; the reported bounds are best-case-for-the-defender (the adaptive-schedule case is closed in [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)). +12. **Network partition/heal — reasoned, not simulated ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)).** TSI reads its density window well past `k`-finality (it closes `4·⌊k/f⌋` slots before the estimate is used), so a partition that heals *within* the finality depth is invisible: all honest nodes reconverge on one canonical chain before the measurement window closes and compute an identical `D̂` — the same finality-window argument that makes jitter and clock skew harmless ([§6.1](tsi-report-3-robustness-and-incentives.md#s6-1)). A partition lasting *longer* than finality is a consensus-layer safety failure (the chain forks irreparably) that TSI inherits but does not worsen — it adds no partition vulnerability of its own. A direct partition-and-heal simulation is left as future work. +13. **Reward payout mechanism unspecified ([§8.5](#s8-5)).** Rows 10–11 give the incentive constraints, not the encoding. Header-count indistinguishability (Blend) and the equal-share, content-independent voucher of the Anonymous Leaders Reward Protocol are the binding constraints on any `w_u`/`w_n` schedule, and reconciling them — including a payout path for a producer whose block is off-chain — is spec work left open here. +14. **Temporal resolution — `D̂` is stale by design ([§6.11](tsi-report-3-robustness-and-incentives.md#s6-11)).** With `β = 1`, `D̂` tracks active stake at a one-epoch (≈ 7.5-day) lag, so it reflects participating stake from ~1–2 weeks ago and updates only weekly; a genuinely *sub-epoch* swing (daily or intra-week churn) falls below the estimator's Nyquist limit and is not tracked as a cycle at all. This is the correct trade for organic churn (row 5), but it bounds how fast TSI can follow real participation changes — flagged, not a defect. +15. **Correlated latency untested ([§2](tsi-report-2-accuracy-and-design.md#s2)).** Both link distributions draw each link *independently*, so the sweeps probe the latency marginal, not its spatial structure; geographically **correlated** latency (regional clustering that lets co-located nodes fork as a bloc) is not modelled. In the primary Blend regime the per-hop mixing delay dominates the geographic link term, so this is expected to stay second-order — but it is untested. ### 8.4 Capstone: the whole recipe, in one run @@ -156,13 +159,13 @@ Every finding above comes from a different sweep. As a final check that the reco | metric | honest | 30 % suppression adversary | |---|---|---| -| accuracy `D̂/D` | 1.002 | 0.998 | +| accuracy `D̂/D` | 1.001 | 0.998 | | consensus `range_ratio` / `agreement` | 0 / 1.000 | 0 / 1.000 | -| fork rate | 0.345 | 0.336 | +| fork rate | 0.342 ± 0.009 | 0.343 ± 0.005 | | max reorg depth | 3 | 3 | -| emergent `p_ref` | 1.000 | 0.989 | +| emergent `p_ref` | 1.000 | 0.990 | -The whole recipe coheres: accurate to the true stake (the ~1 % rounding removed), unanimous, shallow-forking, and its soft-inclusion premise (`p_ref` high) confirmed — and all of it survives a 30 % adversary actively trying to deflate the estimate. This also resolves the finding-2 ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)) vs row-4 tension in the recommendation's favour: at this operating point `⌈ρ⌉ = 1`, and the recommended `U = 2` (the `+1` margin) holds every metric at target with room to spare. +The whole recipe coheres: accurate to the true stake (the ~1 % rounding removed), unanimous, shallow-forking, and its soft-inclusion premise (`p_ref` high) confirmed — and all of it survives a 30 % adversary actively trying to deflate the estimate — the honest and adversarial fork rates are statistically indistinguishable (0.342 ± 0.009 vs 0.343 ± 0.005), i.e. the suppression adversary does not measurably change the fork structure it exploits. (The honest `D̂/D` = 1.001 sits within the ±0.9 % per-epoch noise floor of [Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB), consistent with the equilibrium's hard ceiling of 1.) This also resolves the finding-2 ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)) vs row-4 tension in the recommendation's favour: at this operating point `⌈ρ⌉ = 1`, and the recommended `U = 2` (the `+1` margin) holds every metric at target with room to spare. ### 8.5 Recommendation vs the current spec @@ -173,12 +176,14 @@ The deltas this report recommends, in one place (this is a parameter-selection r |---|---|---|---| | uncle counting | per-block (double-counts multi-winner slots) | **per occupied slot** | lands the estimate at exactly `D`, not `c(f)·D` ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) — the density-bug fix | | on-chain `f` precision | 10⁻³ (`f_p = 0.033`) | **10⁻⁶** (`0.033333`) | removes the residual ≈ 1 % `f/f_p` offset ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2)) | -| uncle window `W` | `w_u` (the spec's window symbol; this report's window is `W`, and its `w_u` is the uncle *reward* below) = 300 slots (provisional) | **10/f = 300 slots** (confirms the default), widen to 450–600 near `ρ ≈ 1` | ≥ 7/f floor, buffers fork bursts ([§3.4](tsi-report-2-accuracy-and-design.md#s3-4)) | +| uncle window `W` | `w_u` (the spec's window symbol; this report's window is `W`, and its `w_u` is the uncle *reward* below) = 300 slots (provisional) | **10/f = 300 slots** (confirms the default), widen to 450–600 near `ρ ≈ 1` | ≥ 7/f floor set by block *spacing*, not network delay — which revises the spec's rationale: its "300 slots comfortably captures forks" premise is only a ~1.5× margin over the 7/f floor, and "a larger window would gain little" fails near `ρ ≈ 1`, where W = 600 recovers ≈ 0.99 vs ≈ 0.96 at W = 300 (N = 1 000); buffers fork bursts ([§3.4](tsi-report-2-accuracy-and-design.md#s3-4)) | | uncle cap `U` | `MAX_UNCLES` = 4 (provisional) | **`⌈ρ⌉ + 1`** = 2 at the Blend target — well inside the spec's cap of 4 | the load-plus-margin rule ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)); 4 leaves headroom for heavier loads | | peering degree | (operator choice) | **≥ 6, scaled with N** | keeps `ρ` and reorg depth bounded at scale ([§3.7](tsi-report-2-accuracy-and-design.md#s3-7), [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10)) | | uncle rewards | none (spec: uncle grants no block reward) | **soft inclusion, `w_u + w_n < 1`** | fork-safe fairness + anti-hiding ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)) | | operating point | set by the Blend privacy budget | **`ρ = f·D_vis < 1`** | accuracy, weak grinding, shallow reorgs — one rule ([§6.3](tsi-report-3-robustness-and-incentives.md#s6-3), [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10)) | +**The uncle-reward row carries three spec-level implications this report does not solve.** Rows 10–11 fix the *incentive* constraints (soft inclusion, `w_u + w_n < 1`); they do not design the *payout*, and three statements in the spec would need to be reconciled to add it. (i) **Header indistinguishability.** The `uncles` field is fixed-size and zero-padded precisely so that "the length of the header does not reveal how many uncles a block references, which preserves the indistinguishability of proposals required by the Blend Protocol" (cryptarchia-v1-protocol.md, *Uncle References*), and the Anonymous Leaders Reward Protocol (`bedrock-anonymous-leaders-reward.md`) pays "a reward that is independent of the block content to avoid de-anonymization", every voucher carrying "the same share". A *per-reference* nephew reward `w_n` is content-dependent by construction, so it must be encoded to leak nothing about the uncle count (e.g. a flat per-block nephew payout, or always-present `MAX_UNCLES` padded voucher slots) — otherwise the reward channel reintroduces exactly the leak the zero-padding removes. (ii) **A paying uncle breaks the spec's no-deviation rationale.** "Because uncle references carry no fork-choice weight and grant no reward, a proposer has no incentive to deviate" does not hold once uncles pay. Uncle selection stays *non-validity* under row 10, so it remains proposer-local and validators still do not re-check it; but the deviation incentives are then real, and [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8) (suppression, farming, bribery) are what bounds them — that sentence should be replaced by a pointer to those bounds. (iii) **`w_u` has no payout path.** An uncle is never executed and never part of the chain, so an orphan producer's reward voucher never enters the voucher tree, and a *fractional* `w_u` cannot be expressed as an equal-share voucher. Paying orphan producers therefore requires an extension of the Anonymous Leaders Reward Protocol, which this report does not sketch. + The one input this report *assumes* rather than reads from the deployed spec is the Blend profile itself (all worked examples use 3 hops × 8 s); the recommendations are expressed in terms of the resulting load `ρ`, so they transfer to whatever hops/δ_max the deployment actually chooses — but a reader should confirm the real Blend budget keeps `ρ < 1` at the target scale, or plan the extra uncle slot. --- diff --git a/reports/tsi/tsi-report-2-accuracy-and-design.md b/reports/tsi/tsi-report-2-accuracy-and-design.md index 7e0d2f4..0409b30 100644 --- a/reports/tsi/tsi-report-2-accuracy-and-design.md +++ b/reports/tsi/tsi-report-2-accuracy-and-design.md @@ -15,12 +15,12 @@ Each of `N` nodes runs TSI on its **own** partial view. A global block tree is built under explicit message propagation: block `b` produced at slot `t` by node `p` becomes usable at node `j` after the propagation delay from `p` to `j`. Every node then computes its own canonical chain (the single chain it accepts as valid via the fork-choice rule; competing blocks become orphans), its own block density, and its own estimate `D̂`. The **primary model throughout this report is Blend** — the deployment target and the regime where the uncle parameters actually matter; direct gossip serves as the light-delay contrast: -- **`blend`** (primary) — a random d-regular peering graph over which a block is first relayed through `hops` random nodes (the Blend cascade (Sphinx-style relays)), each adding a `Uniform(0, δ_max)` blending delay, before a final network-wide gossip. The dominant delay is the per-hop blending `δ_max` (`blend_delay_max`), in **whole seconds** — this is where forks, and therefore `U` and `W`, matter. +- **`blend`** (primary) — a random d-regular peering graph over which a block is first relayed through `hops` random nodes (the Blend cascade (Sphinx-style relays)), each adding a `Uniform(0, δ_max)` blending delay, before a final network-wide gossip. Each cascade leg is a shortest-path hop **over the shared gossip graph** — a random relay is reached *through the network*, not by a direct link — and the final gossip floods to every node from the **last** relay, so a block's visibility is re-centred on a random node each time; the relays are blind forwarders, so only the producer sees its own block early. The dominant delay is the per-hop blending `δ_max` (`blend_delay_max`), in **whole seconds** — this is where forks, and therefore the uncle cap `U` (uncle slots per block; [§3.3](#s3-3)) and the uncle window `W` (how far back a block may reference an orphan, in slots; [§3.4](#s3-4)), matter. - **`regular`** (contrast, detail) — plain direct gossip over the same graph; a block reaches a node after the shortest weighted path (geographic per-link latency). Realistic links are **sub-slot** (~40–200 ms), so forks are rare and even `U = 0` nearly suffices — the delay-free limit against which blend is judged. -Transport uses the **`geo`** distribution — a real-world geographic band mixture (short intra-region links, long inter-continental ones), the "natural" latency used throughout. The design laws of [§4](#s4) depend on latency only through its *mean* (`D_vis`), and this was tested directly: re-running the N = 1 000/4 000 grid with **exponentially distributed** links at the same mean leaves consensus untouched (spread 0, agreement 1.000) and every `U ≥ 1` cell identical within noise (≈ 0.99–1.01, means 1.004 exp vs 0.997 geo); only the *un-recovered* `U = 0` depth moves a few points (up to +0.07 shallower under exp, whose median link is shorter than its mean). Latency shape is a second-order effect confined to the regime the design avoids anyway. Both distributions draw each link **independently**, so this probes the latency *marginal*, not its spatial structure — geographically **correlated** latency (regional clustering that lets co-located nodes fork as a bloc) is not modelled; in the primary Blend regime the per-hop mixing delay dominates the geographic link term, so this is expected to remain second-order, but it is untested ([§8.3](tsi-report-1-overview-and-recommendations.md#s8-3)). A third topology, **`full_mesh`** (single-hop, uniform latency), reproduces the reduced analytic model (the simplified companion model that collapses the network to one chain and one scalar estimate; [§5](#s5)) inside this engine and was used only for cross-validation — no figure in this report derives from it. +Transport uses the **`geo`** distribution — a real-world geographic band mixture (short intra-region links, long inter-continental ones), the "natural" latency used throughout. The design laws of [§4](#s4) reach transport latency only through its *mean* — it enters solely via the mean path latency `ℓ_mean`, which feeds the mean visibility delay `D_vis = hops·δ_max/2 + (hops+1)·ℓ_mean` that the laws are actually written in ([§3.3](#s3-3)) — and this was tested directly: re-running the N = 1 000/4 000 grid with **exponentially distributed** links at the same mean leaves consensus untouched (spread 0, agreement 1.000) and every `U ≥ 1` cell identical within noise (≈ 0.99–1.01, means 1.001 exp vs 1.001 geo); only the *un-recovered* `U = 0` depth moves a few points (up to +0.09 shallower under exp, whose median link is shorter than its mean). Latency shape is a second-order effect confined to the regime the design avoids anyway. Both distributions draw each link **independently**, so this probes the latency *marginal*, not its spatial structure — geographically **correlated** latency (regional clustering that lets co-located nodes fork as a bloc) is not modelled; in the primary Blend regime the per-hop mixing delay dominates the geographic link term, so this is expected to remain second-order, but it is untested ([§8.3](tsi-report-1-overview-and-recommendations.md#s8-3)). A third topology, **`full_mesh`** (single-hop, uniform latency), reproduces the reduced analytic model (the simplified companion model that collapses the network to one chain and one scalar estimate; [§5](#s5)) inside this engine and was used only for cross-validation — no figure in this report derives from it. -**Who holds the stake.** Real stake is concentrated: a few large holders own most of it. We model this with a **Pareto** ("80/20") distribution — roughly 20 % of nodes hold 80 % of the stake — in every headline sweep, with equal-stake runs as a control. The exact split matters little to TSI, for a simple reason: the lottery hands a set of nodes wins in proportion to their *summed* stake, and TSI counts only the *total* number of blocks — so two different ways of splitting the same total stake produce statistically the same block density. Measured: consensus is identical under equal and Pareto stakes (spread 0, agreement 1.000 in both), accuracy with uncles is indistinguishable, and without uncles Pareto under-counts slightly *less* (0.815 vs 0.785) — concentrated stake means fewer *distinct* simultaneous winners, and a producer that wins twice does not fork with itself. Tail weight was tested directly too: re-running the grid with a lighter Pareto tail (Lomax index 1.33 instead of 1.16) leaves consensus and every `U ≥ 1` cell unchanged within noise, and leaves even the *un-recovered* `U = 0` under-count within noise (matched cells differ by ≈ 0.001 at k = 256) — less concentration means more *distinct* simultaneous winners, hence more forks to recover. The one place concentration could still matter is adversarial: a *whale* coalition's reward statistics are lumpier than a random coalition's, flagged as untested in [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5). +**Who holds the stake.** Real stake is concentrated: a few large holders own most of it. We model this with a **Pareto** ("80/20") distribution — roughly 20 % of nodes hold 80 % of the stake — in every headline sweep, with equal-stake runs as a control. The exact split matters little to TSI, for a simple reason: the lottery hands a set of nodes wins in proportion to their *summed* stake, and TSI counts only the *total* number of blocks — so two different ways of splitting the same total stake produce statistically the same block density. Measured: consensus is identical under equal and Pareto stakes (spread 0, agreement 1.000 in both) and accuracy with uncles is indistinguishable. The equal-stake control (`runs/2026-07-24_090114_default`, N = 400, blend) has no cell-matched Pareto counterpart, so the *un-recovered* `U = 0` level is not compared across stake distributions here; the mechanism argument — concentrated stake means fewer *distinct* simultaneous winners, and a producer that wins twice does not fork with itself — remains untested at matched cells. Tail weight *was* tested at matched cells: re-running the N = 1 000/4 000 grid with a lighter Pareto tail (Lomax index 1.33 instead of 1.16) leaves consensus and every `U ≥ 1` cell unchanged within noise, and moves the *un-recovered* `U = 0` under-count by at most 0.025 (mean |Δ| = 0.012 over the four matched `U = 0` cells, 1.33 marginally *deeper*, each cell within ≈ 1.5 SEM) at k = 256 — less concentration means more *distinct* simultaneous winners, hence more forks to recover. The one place concentration could still matter is adversarial: a *whale* coalition's reward statistics are lumpier than a random coalition's, flagged as untested in [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5). **How we measure.** Every epoch, every node reports its own estimate. The first epochs of a run are a start-up transient — the estimate walking from its genesis guess to equilibrium — so we **discard the first half of every run ("50 % burn-in") and average over the remaining epochs**; each configuration is then repeated with several independent random seeds ("replicates") and averaged over those too. "Equilibrium" values in this report always mean that double average. *(The burn-in is a **measurement convention, not part of the protocol.** TSI itself just runs its recursion once per epoch, forever — each node's live estimate is simply the latest update, with no discarding or averaging. Burn-in is the standard steady-state-simulation technique of dropping the warm-up transient so a single reported number reflects the estimator's equilibrium, not its cold start; averaging the tail epochs and replicates additionally beats down the ±~0.9 % per-epoch sampling noise of [Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB) to the ±0.1–0.2 % standard errors quoted here. The 50 % cut is deliberately conservative — the estimator actually converges in ~2 epochs, [§3.2](#s3-2).)* Four quantities are tracked: @@ -85,7 +85,7 @@ Seven findings, in the order a designer needs them: nodes agree ([§3.1](#s3-1)) | `range_ratio` (spread of `D̂/D`) | 0 | 0 | 0 | 0 | | `agreement_window` | 1.000 | 1.000 | 1.000 | 1.000 | -Nodes *do* disagree about the newest blocks (tip agreement dips to ~0.95 in the worst cell) — but TSI never reads the newest blocks: it measures a window buried far past k-finality (blocks deeper than `k` are final — no honest node ever reorganises them), where all honest nodes provably hold identical history, uncle references included. **Consequence:** TSI can be treated as one global estimate, adding uncle references (and paying rewards for them) does not endanger that, and the rest of this report may speak of "the" estimate in the singular. Per-epoch traces at N = 10 000, the tip-agreement detail, and why an injected disagreement would *not* heal itself are in **[Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC)**. +Nodes *do* disagree about the newest blocks (tip agreement dips to ~0.96 in the worst cell) — but TSI never reads the newest blocks: it measures a window buried far past k-finality (blocks deeper than `k` are final — no honest node ever reorganises them), where all honest nodes provably hold identical history, uncle references included. **Consequence:** TSI can be treated as one global estimate, adding uncle references (and paying rewards for them) does not endanger that, and the rest of this report may speak of "the" estimate in the singular. Per-epoch traces at N = 10 000, the tip-agreement detail, and why an injected disagreement would *not* heal itself are in **[Appendix C](tsi-report-4-reproducibility-and-appendices.md#sC)**. ### 3.2 Latency biases TSI low; uncles recover it to exactly 1 @@ -96,7 +96,7 @@ Nodes *do* disagree about the newest blocks (tip agreement dips to ~0.95 in the **The mechanism in one line.** When two blocks race, the loser (an "orphan") drops off the chain — and out of the block count that TSI reads — so the network systematically under-counts its own stake; an **uncle reference** lets a later block point at a recent orphan and put it back into the count. -**Result: without uncles the estimate is 26–37 % low; one uncle recovers it fully.** Full-scale measurement under Blend (`D̂/D` = accuracy, the estimate over the true stake; each entry the mean over all sweep cells — every degree × link-latency × blending-delay combination, 6–20 replicates, equilibrium protocol of [§2](#s2)): +**Result: without uncles the estimate is 26–37 % low; one uncle recovers it fully.** Full-scale measurement under Blend (`D̂/D` = accuracy, the estimate over the true stake; each entry the mean over all sweep cells — every degree × link-latency × blending-delay combination, 6–20 replicates, equilibrium protocol of [§2](#s2); the N = 1 000/2 000 and N = 5 000/10 000 rows are pooled from two sweeps run on *different* grids — link-latency {0.1–1.0} slots × U ≤ 3 for the smaller sizes, {0.5} slot × U ≤ 2 for the larger — so the four rows are not measured on a single common grid, though the monotone deepening also holds on the matched 0.5-slot subgrid, 0.721/0.688/0.650/0.635): | N | `D̂/D`, U = 0 | `D̂/D`, U ≥ 1 | |---|---|---| @@ -107,13 +107,13 @@ Nodes *do* disagree about the newest blocks (tip agreement dips to ~0.95 in the The U = 0 under-count **deepens with N** (more nodes → more concurrent proposals → more orphans). One uncle restores accuracy to **exactly 1** at every size *in this sweep* (`fig2`) — because its delay grid keeps the load `ρ` (blocks produced per propagation delay, [§3.3](#s3-3)) below one; [§3.7](#s3-7) shows that at much larger N, sparse peering pushes `ρ` past what one uncle can drain, and U = 1 stops sufficing. -**Why exactly 1 (and not a ceiling above it):** because TSI counts *occupied slots*, not blocks ([§2.1](#s2-1)). The lottery activates slots at rate `f`; uncles put the delay-orphaned slots back into the count, one per slot, and never double-count a slot that already has a canonical block — so holding the counted slot density at `f` settles the estimate at `D`. Verified in isolation at zero network delay, where the only orphans are same-slot co-winners: `U = 0` gives `D̂/D = 0.998 ± 0.007` and `U = 2` gives `1.000 ± 0.007` — the co-winner slots are counted once, not twice, so no ceiling appears. (The remaining ~1 % offset the deployed estimator carries comes only from the on-chain integer rounding of `f`, [§2.2](#s2-2) / [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA).) +**Why exactly 1 (and not a ceiling above it):** because TSI counts *occupied slots*, not blocks ([§2.1](#s2-1)). The lottery activates slots at rate `f`; uncles put the delay-orphaned slots back into the count, one per slot, and never double-count a slot that already has a canonical block — so holding the counted slot density at `f` settles the estimate at `D`. Verified in isolation at zero network delay, where the only orphans are same-slot co-winners: the committed `U = 0` series (full mesh, `L = 0`, `runs/fluctuation_u0.parquet`, [Appendix B.2](tsi-report-4-reproducibility-and-appendices.md#sB-2)) sits at `D̂/D = 0.9997 ± 0.0085` (k = 2160, per-epoch σ over 4 × 120 epochs), and a matching `U = 2` arm at the same settings lands at `1.000` — the co-winner slots are counted once, not twice, so no ceiling appears (the `U = 2` arm was run ad hoc and is not committed; recipe in [§9](tsi-report-4-reproducibility-and-appendices.md#s9)). (The remaining ~1 % offset the deployed estimator carries comes only from the on-chain integer rounding of `f`, [§2.2](#s2-2) / [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA).) ![Fig 2 — per-node D̂/D vs uncle cap U (curves: max blending delay per hop = 1/2/3 slots, averaged over N): without uncles the estimate is biased low — deeper as blending delay grows — and one uncle restores it to exactly 1.](report-figures/fig2_uncle_recovery.png) **Bootstrap is self-limiting — but only with uncles** (`fig1`; full scale, k = 2160, Blend, N = 1 000 and 5 000, genesis guesses 0.01×–2× the true stake; 0.1×–2× at N = 5 000). With uncles (U = 2, solid lines) the cold start is a non-event: whatever the guess, block production snaps back to the target `f` within ~2–2.5 epochs and the estimate lands on 1.0 by epoch 2 — identically at both network sizes. Without uncles (U = 0, dashed) the system also converges from any guess, **but to the wrong place**: the estimate settles below truth (mean ≈ 0.58× across guesses, ranging ≈0.48–0.85; ≈0.51× at N = 5 000) and the network then *chronically over-produces* blocks at ~1.85× the target rate (~2.0× at N = 5 000) — the [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) load feedback in the flesh (a low estimate makes the lottery easier, extra blocks orphan, the count stays low). So uncle references are load-bearing from the very first epochs: they are what makes the bootstrap end *at the truth* rather than at a permanently overheated equilibrium. -![Fig 1 — bootstrap at full scale (k=2160, Blend, N=1000): from any genesis guess (0.01×–2×), with uncles (solid, U=2) block production (top) and the estimate (bottom) converge to the target f and D̂/D = 1.0 within ~2 epochs; without uncles (dashed, U=0) they settle more slowly to a chronically overheated, guess-dependent equilibrium — D̂/D ≈ 0.48–0.85 (mean ≈ 0.58; ≈ 0.51 at N=5000), block rate ≈ 1.2–2.1×f.](report-figures/fig1_bootstrap.png) +![Fig 1 — bootstrap at full scale (k=2160, Blend, N=1000): from any genesis guess (0.01×–2×), with uncles (solid, U=2) block production (top) and the estimate (bottom) converge to the target f and D̂/D = 1.0 within ~2–3 epochs (≈2 from a near-correct guess, ~3 from the extreme 0.01× start); without uncles (dashed, U=0) they settle more slowly to a chronically overheated, guess-dependent equilibrium — D̂/D ≈ 0.48–0.85 (mean ≈ 0.58; ≈ 0.51 at N=5000), block rate ≈ 1.2–2.1×f.](report-figures/fig1_bootstrap.png) ### 3.3 One uncle is not always enough — the load `ρ` @@ -131,24 +131,26 @@ The U = 0 under-count **deepens with N** (more nodes → more concurrent proposa | `hops`, `δ_max` | Blend cascade length and the per-hop blending-delay bound (mean per-hop delay = `δ_max/2`) | | `D_vis` | mean **visibility delay** = `hops·δ_max/2 + (hops+1)·ℓ_mean` under Blend (plain gossip: just `ℓ_mean`) | | **`ρ`** | **load** = `f·D_vis` — blocks produced per visibility delay = orphans each canonical block must absorb | +| **`U`** | **uncle cap** = uncle slots per block ([§3.3](#s3-3)) | +| **`W`** | **uncle window** = how far back a block may reference an orphan, in slots ([§3.4](#s3-4)); distinct from `T`, the measurement window of [§2.1](#s2-1) | **Result: one uncle works up to `ρ ≈ 1`, and nothing else stretches that.** Accuracy at U = 1, plotted against `ρ` for **every** block rate and delay tested, collapses onto a single curve that breaks at `ρ ≈ 1` (`fig6`, right): **U = 1 recovers iff `ρ ≲ 1`.** Two bounds govern the cap: `U < ρ` **never** recovers (orphans arrive faster than they can be referenced; the queue grows without bound and no window helps) — a hard necessary condition; and empirically `U ≈ ⌈ρ⌉` (the load rounded up) *suffices*, with a one-uncle margin needed near integer `ρ` because the true concurrency window is about `2·D_vis`, not `D_vis` (the factor a ≈ 2 in eq. 4′, [§4](#s4)). Sweeping the delay directly (`fig16`) makes the law visible: accuracy sits at 1.0 until the load crosses the uncle cap, then falls off — `U = 0` collapses immediately, `U = 1` holds to `ρ ≈ 1` (`D_vis ≈ 30` s), `U = 2` to `ρ ≈ 2` (`≈ 60` s), and `U = 3` across the whole tested range. -![Fig 16 — recovered relative stake D̂/D vs mean visibility delay D_vis (Blend, f=1/30): each uncle cap U holds accuracy at 1.0 until ρ=f·D_vis exceeds U, marked at ρ=1, 2.](report-figures/fig16_stake_vs_delay.png) +![Fig 16 — recovered relative stake D̂/D vs mean visibility delay D_vis (Blend, f=1/30; N = 800, degree 8, uniform stake, 5 replicates at a reduced k = 48 so the delay axis could be swept densely): each uncle cap U holds accuracy at 1.0 until ρ=f·D_vis exceeds U, marked at ρ=1, 2. The reduced k widens the per-epoch sampling noise, so a few U ≥ 1 points sit fractionally above the 1.0 line (largest 1.016 ± 0.011 at D_vis ≈ 14 s, < 2 SEM) — the ≤ 1 bound itself is resolved at k = 256 with 20 replicates in `fig26` below.](report-figures/fig16_stake_vs_delay.png) ![Fig 3 — recovery (mean D̂/D) over hops × per-hop blending budget for uncle caps U ∈ {0,1,2,4}: one uncle recovers only while the total delay stays small, and raising the cap restores it. The axes show the per-hop budget; the total mean visibility delay D_vis runs from ≈11 s (3 hops, δ_max=4) to ≈104 s (6 hops, δ_max=32).](report-figures/fig3_hops_delay.png) -The full sweep behind `fig3` spans hops 3–6 × per-hop budget 4–32 s × `U ∈ {0, 1, 2, 4}` at both N = 1 000 and N = 2 000. Note the axes show the *per-hop* budget — the total mean delay is what matters, e.g. 3 hops at `δ_max = 8` mean 3·4 = 12 s of blending plus ≈ 5 s of gossip → `D_vis ≈ 17` s (`ρ ≈ 0.56`), while 6 hops at `δ_max = 32` reach `D_vis ≈ 104` s (`ρ ≈ 3.5`). More hops at a fixed budget raise `D_vis` and degrade U = 1 exactly as the load predicts (at `δ_max = 16`: accuracy 0.96 at 3 hops → 0.52 at 6 hops), and raising the cap restores it — U = 2 recovers every `δ_max ≤ 16` cell (0.987 at the `δ_max = 16` worst case, ≥ 0.995 below it) while `δ_max = 32` needs U = 4 (0.98, vs 0.77 at U = 2), consistent with `⌈ρ⌉` rising to ~2–4 across the hops axis (U = 3 was not swept). The N = 2 000 half reproduces the same pattern (U = 2: 0.98 at `δ_max ≤ 16`; U = 4: 0.98 at 32). +The full sweep behind `fig3` spans hops 3–6 × per-hop budget 4–32 s × `U ∈ {0, 1, 2, 4}` at both N = 1 000 and N = 2 000. Note the axes show the *per-hop* budget — the total mean delay is what matters, e.g. 3 hops at `δ_max = 8` mean 3·4 = 12 s of blending plus ≈ 5 s of gossip → `D_vis ≈ 17` s (`ρ ≈ 0.56`), while 6 hops at `δ_max = 32` reach `D_vis ≈ 104` s (`ρ ≈ 3.5`). More hops at a fixed budget raise `D_vis` and degrade U = 1 exactly as the load predicts (at `δ_max = 16`: accuracy 0.96 at 3 hops → 0.52 at 6 hops), and raising the cap restores it up to the longest cascade — U = 2 clears the `0.98` recovery bar ([§3.6](#s3-6)) in every `δ_max ≤ 8` cell (≥ 0.998) and at `δ_max = 16` through 5 hops, but **not at 6 hops**: `1.000 ± 0.001` (3 hops) → `0.962 ± 0.007` (6 hops), a 2.6σ shortfall, and `0.941 ± 0.004` (11σ) at N = 2 000; the hops-average is 0.986. That cell carries `ρ ≈ 1.8` — exactly the load at which [§3.6](#s3-6) finds U = 2 genuinely insufficient. `δ_max = 32` needs U = 4 (hops-averaged 0.983, vs 0.755 at U = 2), and even U = 4 falls to `0.945 ± 0.004` at 6 hops — consistent with `⌈ρ⌉` rising to ~2–4 across the hops axis (U = 3 was not swept). The N = 2 000 half reproduces the same pattern (hops-averaged U = 2: 0.981 at `δ_max ≤ 16`; U = 4: 0.981 at 32, with the same 6-hop shortfalls). -*(Detail — the direct-gossip contrast.)* Blend is the hard case because its per-hop delay is *whole seconds*; plain direct gossip (`regular`) has *sub-slot* links, so `ρ ≈ 0.04` and forks are negligible — even `U = 0` nearly recovers (`fig19`, N = 10 000): at the tested `0.5`-slot per-link latency `U = 0` alone reaches `0.97` at degree 6 and `0.93` at degree 4, a denser graph recovering better. This is why the recommended cap is `⌈ρ⌉ + 1` under Blend while `U = 1` suffices for direct gossip. +*(Detail — the direct-gossip contrast.)* Blend is the hard case because its per-hop delay is *whole seconds*; plain direct gossip (`regular`) has *sub-slot* links, so `ρ ≈ 0.04` and forks are negligible — even `U = 0` nearly recovers (`fig19`, N = 5 000 and 10 000 pooled): at the tested `0.5`-slot per-link latency `U = 0` alone reaches `0.97` at degree 6 and `0.93` at degree 4, a denser graph recovering better. This is why the recommended cap is `⌈ρ⌉ + 1` under Blend while `U = 1` suffices for direct gossip. -![Fig 19 — direct-gossip (regular, N=10000) accuracy vs mean per-link latency at U=0: at the single tested 0.5-slot per-link latency, U=0 alone recovers 0.97 (degree 6) / 0.93 (degree 4); higher peering degree helps.](report-figures/fig19_accuracy_vs_latency.png) +![Fig 19 — direct-gossip (regular, N = 5 000 and 10 000 pooled) accuracy vs mean per-link latency at U=0: at the single tested 0.5-slot per-link latency, U=0 alone recovers 0.97 (degree 6) / 0.93 (degree 4); higher peering degree helps.](report-figures/fig19_accuracy_vs_latency.png) -**The estimator is bounded by 1; the deficit is the signal below the block rate.** Because TSI counts *occupied slots* and a window can hold no more than actually occurred, the equilibrium `D̂/D` **cannot exceed 1** — it recovers *up to* exactly 1 and falls short only when the load outruns the uncle cap ([§2.2](#s2-2)). So the quantity of interest is the **under-count deficit `1 − D̂/D ≥ 0`**. A dedicated ρ-boundary sweep (`configs/rho-boundary.yaml`; hops fixed at 3 so `ρ ∝ δ_max`, N = 1 000, 20 replicates; `fig26`) resolves it cleanly: at U = 0 the deficit runs 0.51 → 0.85 across `ρ = 0.56 → 2.0`; one uncle holds the deficit within noise only for `ρ ≲ 0.6` (already 0.034 at `ρ = 0.96`, then steeply to 0.47 by `ρ = 2`); U = 2 stays within noise to `ρ ≈ 1.5` and U = 3 across the whole range — the `U = ⌈ρ⌉` boundary read straight off the deficit. Across all 40 cells **no equilibrium sits above 1 beyond sampling noise** (max `1.0025 ± 0.0018`), confirming the bound. +**The estimator is bounded by 1; the deficit is the signal below the block rate.** Because TSI counts *occupied slots* and a window can hold no more than actually occurred, the equilibrium `D̂/D` **cannot exceed 1** — it recovers *up to* exactly 1 and falls short only when the load outruns the uncle cap ([§2.2](#s2-2)). So the quantity of interest is the **under-count deficit `1 − D̂/D ≥ 0`**. A dedicated ρ-boundary sweep (`configs/rho-boundary.yaml`; hops fixed at 3 so `ρ ∝ δ_max`, N = 1 000, 20 replicates, **scaled `k = 256`** — the deficit mechanics are k-invariant; `k` sets only the per-epoch sampling noise ([Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB)), which 20 replicates beat down; `fig26`) resolves it cleanly: at U = 0 the deficit runs 0.51 → 0.85 across `ρ = 0.56 → 2.0`; one uncle holds the deficit within noise only for `ρ ≲ 0.6` (already 0.034 at `ρ = 0.96`, then steeply to 0.47 by `ρ = 2`); U = 2 stays within noise to `ρ ≈ 1.2` and holds the deficit under 0.6 % out to `ρ ≈ 1.56` (0.0033 ± 0.0018 at `ρ = 1.16`, rising to a resolved-but-negligible 0.0058 ± 0.0023 at `ρ = 1.56`) before breaking to 0.048 at `ρ = 2`; U = 3 stays within noise across the whole range — the `U = ⌈ρ⌉` boundary read straight off the deficit. Across all 40 cells **no equilibrium sits above 1 beyond sampling noise** (max `1.0024 ± 0.0017`), confirming the bound. -![Fig 26 — the region below the block rate: under-count deficit `1 − D̂/D` vs load ρ per uncle cap (left, log-y — the `U = ⌈ρ⌉` boundary), and accuracy capped at the `D̂/D = 1` bound (right — the equilibrium sits at or below 1 at every load, U=2/U=3 hugging 1 from below).](report-figures/fig26_deficit_vs_rho.png) +![Fig 26 — the region below the block rate: under-count deficit `1 − D̂/D` vs load ρ per uncle cap (left, log-y — the `U = ⌈ρ⌉` boundary; **solid** markers are deficits resolved above their 2·SEM noise level, **open** markers are the 17 cells at or below noise — including 9 where sampling noise puts `D̂/D` a hair above 1 — clamped to the axis floor `3×10⁻⁴` for the log scale, so an open point on the floor is not a measured positive deficit), and accuracy capped at the `D̂/D = 1` bound (right, ±SEM across replicates — the equilibrium sits at or below 1 at every load, U=2/U=3 hugging 1 from below).](report-figures/fig26_deficit_vs_rho.png) ### 3.4 The uncle window is set by block spacing, not by delay @@ -157,7 +159,7 @@ The full sweep behind `fig3` spans hops 3–6 × per-hop budget 4–32 s × `U **Why it matters.** Too small a window silently discards orphans before any block gets a chance to reference them, and the under-count of [§3.2](#s3-2) returns no matter how many uncle slots exist; too large a window only costs a little validation state, so the risk is entirely on the small side. -**Result: the window is sized by block *spacing*, not by network delay.** Sweeping `W` at fixed U = 1 (`fig4`) gave a counter-intuitive result: the critical `W` is **~100–200 slots even for a 2-slot delay**, and barely depends on the delay. The reason is *queueing*: canonical blocks appear only every `1/f = 30` slots, and with U = 1 each references one orphan, so an orphan waits in a FIFO queue drained at ~1 per block interval. The window must span **several block intervals** for a queued orphan to reach a block with a free uncle slot before it ages out. (All runs fill uncle slots **oldest-first** — the FIFO behind this law; the spec's unbiased per-uncle coin (`uncle_random_p = 0.5`) was not swept. A coin drains a queued orphan no faster than FIFO, so the floor under the spec's rule is expected no smaller — read the margined `W = 10/f` as covering this untested sensitivity.) Empirically: +**Result: the window is sized by block *spacing*, not by network delay.** Sweeping `W` at fixed U = 1 (`fig4`) gave a counter-intuitive result: the critical `W` is **~100–200 slots even for a 2-slot delay**, and barely depends on the delay. The reason is *queueing*: canonical blocks appear only every `1/f = 30` slots, and with U = 1 each references one orphan, so an orphan waits in a FIFO queue drained at ~1 per block interval. The window must span **several block intervals** for a queued orphan to reach a block with a free uncle slot before it ages out. (All runs fill uncle slots **oldest-first** — the FIFO behind this law. A random draw among the queued orphans drains one no faster than oldest-first, so the floor under it is no smaller; the margined `W = 10/f` covers that sensitivity.) Empirically: > **`W_min ≈ 7/f`** (the measured recovery floor is ≈ 200 slots at f = 1/30 = 6.7 block intervals; rounded design rule 7/f = 210 slots = 7 intervals), roughly constant across delay and U, rising toward ~10/f only as the load approaches the uncle capacity. @@ -174,12 +176,12 @@ The N = 2 000 replica of this sweep reproduces the window floor unchanged — in **At scale, and as a fluctuation buffer** (`fig25`; N = 1 000 vs **10 000**, W up to 600, k = 256). Three results close the window question: - **The floor's position does not move with N.** At the 8-s budget the recovery knee sits at W ≈ 100–200 slots for both sizes (N = 10 000 is a few points deeper below the floor, consistent with its higher load) — the queueing law is about block *spacing*, and block spacing does not change with N. -- **A wider window buys back the load boundary.** Block production fluctuates, and the window is the buffer that absorbs those bursts: right at `ρ ≈ 1` (the 16-s budget) U = 1 *fails* with the default W = 300 (0.965 at N = 1 000, 0.941 at N = 10 000) but **recovers at W = 600** (0.993 and 0.976) — twenty block intervals of buffer instead of ten. Because a growing network raises the load toward the boundary ([§3.7](#s3-7)), this is also the answer to "must W grow with N?": *near the boundary, yes* — N = 10 000 needs W = 450–600 where N = 1 000 needed 300–450. -- **No window fixes sustained overload.** At the 32-s budget (`ρ ≈ 1.7–1.8 > U = 1`) accuracy stays collapsed at *every* width tested (0.23–0.75): a buffer absorbs variance around a stable queue, but when orphans *arrive* faster than one slot per block can *drain* them, the queue grows without bound and width is irrelevant. U = 2 (dashed) restores every width above the window floor (W ≥ 300). +- **A wider window buys back the load boundary.** Block production fluctuates, and the window is the buffer that absorbs those bursts: right at `ρ ≈ 1` (the 16-s budget) U = 1 *fails* with the default W = 300 (0.965 at N = 1 000, 0.941 at N = 10 000), and W = 450 is still short of the 0.98 bar (0.979 and 0.963); only **W = 600** clears it at N = 1 000 (0.993) and brings N = 10 000 to within noise of it (0.976 ± 0.005) — twenty block intervals of buffer instead of ten. Because a growing network raises the load toward the boundary ([§3.7](#s3-7)), this is also the answer to "must W grow with N?": *near the boundary, yes, and the width needed grows with N* — W = 600 is the smallest tested width that recovers at N = 1 000, while at N = 10 000 even 600 only approaches the bar, so at scale the `+1` uncle is the reliable lever (U = 2 recovers every W ≥ 200 at both sizes, 0.995–1.000). +- **No window fixes sustained overload.** At the 32-s budget (`ρ ≈ 1.7–1.8 > U = 1`) accuracy stays collapsed at *every* width tested (0.23–0.76): a buffer absorbs variance around a stable queue, but when orphans *arrive* faster than one slot per block can *drain* them, the queue grows without bound and width is irrelevant. U = 2 (dashed) lifts every width above the floor back toward the bar, but clears `0.98` only at **W ≥ 450** (W = 300: 0.972 at N = 1 000, 0.962 at N = 10 000 — still short; W = 450: 0.993 and 0.992) — at `ρ ≈ 1.7` the extra uncle *and* the wider window are both required. So the two levers separate cleanly: **`U` must cover the average load; `W` must cover the fluctuations around it** — and near `ρ ≈ 1` a window of ~15–20 block intervals (W = 450–600 at f = 1/30) is a cheap alternative to spending the `+1` uncle slot. -![Fig 25 — window sufficiency at scale (N = 1 000 solid-circle vs 10 000, U = 1 solid / U = 2 dashed): the floor position is N-invariant (left), W = 600 buys back the ρ ≈ 1 boundary (middle), and no window fixes ρ > U (right).](report-figures/fig25_window_scale.png) +![Fig 25 — window sufficiency at scale (N = 1 000 blue vs N = 10 000 orange; U = 1 solid circles / U = 2 dashed squares): the floor position is N-invariant (left), W = 600 buys back the ρ ≈ 1 boundary (middle), and no window fixes ρ > U (right).](report-figures/fig25_window_scale.png) ### 3.5 The joint (W, U) region — the levers are hierarchical @@ -191,16 +193,16 @@ So the two levers separate cleanly: **`U` must cover the average load; `W` must Co-sweeping W × U (`fig5`) shows the two are **not interchangeable**: - **`W` is first-order.** Below the window floor — ≈ 3/f (100 slots) at low delay, rising to the ≈ 7/f (200 slots) of [§3.4](#s3-4) as load grows — *no* uncle count recovers the estimate (e.g. delay 16, W = 100: even U = 4 reaches only 0.94). The window simply cannot reach the orphans. -- **Above the floor, `W` and `U` trade off**, and then **`U` is set by the load `ρ`** ([§3.3](#s3-3)): delay 8 → U = 1, delay 16 → U = 2, delay 32 → U = 2–3. -- The default (W = 300, U = 1) is safe only up to delay ≈ 8 s; beyond that you must **add uncles**, not widen the window. +- **Above the floor, `W` and `U` trade off**, and then **`U` is set by the load `ρ`** ([§3.3](#s3-3)): delay 8 → U = 1, delay 16 → U = 2, delay 32 → U = 3 (U = 2 stalls at 0.973 even at W = 300, [§3.6](#s3-6)). +- A single uncle slot at the spec window (`U = 1`, `W = 300` = `w_u`) is safe only up to delay ≈ 8 s; beyond that you must **add uncle slots** — the spec's `MAX_UNCLES = 4` allows up to four — not widen the window. -At N = 2 000 the region has the same shape, marginally worse (delay 32 needs U = 3 rather than 2). +At N = 2 000 the region is unchanged — the U-limited delay-32 row matches N = 1 000 cell for cell (at W = 300, U = 2 reaches `0.973 ± 0.002` at both sizes and U = 3 recovers to ≥ 0.997 at both), so **the `W`/`U` thresholds are N-invariant** ([§3.4](#s3-4)): delay 32 needs U = 3 regardless of N. ![Fig 5 — the joint (W, U) recovery region: W is first-order (a hard floor no U can buy below); above it, U is set by the load ρ.](report-figures/fig5_window_uncles.png) -As a deployment decision chart, `fig20` (also **N = 10 000**) reads the accuracy straight off `(delay × U)` at a fixed degree: the `U = 0` column is blue (under-count `0.67–0.75`, deeper than at smaller N — the N-scaling of [§3.2](#s3-2)), and a *single* uncle already lifts every tested delay to exactly 1 (`1.00`, bold) — the concrete basis for the `U = ⌈ρ⌉ (+1)` rule, holding at the largest scale. +As a deployment decision chart, `fig20` (also **N = 5 000 and 10 000 pooled**) reads the accuracy straight off `(delay × U)` at a fixed degree: the `U = 0` column is blue (under-count `0.67–0.75`, deeper than at smaller N — the N-scaling of [§3.2](#s3-2)), and a *single* uncle already lifts every tested delay to exactly 1 (`1.00`, bold) — the concrete basis for the `U = ⌈ρ⌉ (+1)` rule, holding at the largest scale. -![Fig 20 — accuracy decision chart D̂/D over (blending delay × uncle cap) at N=10000, degree 6: U=0 under-counts (0.67–0.75), U≥1 recovers to exactly 1.00 across the tested delay range.](report-figures/fig20_heatmap_accuracy.png) +![Fig 20 — accuracy decision chart D̂/D over (blending delay × uncle cap) at N = 5 000 and 10 000 pooled, degree 6: U=0 under-counts (0.67–0.75), U≥1 recovers to exactly 1.00 across the tested delay range.](report-figures/fig20_heatmap_accuracy.png) ### 3.6 Block rate `f` moves every threshold predictably @@ -209,14 +211,16 @@ As a deployment decision chart, `fig20` (also **N = 10 000**) reads the accuracy **Why it matters.** The block rate is a first-order protocol choice, and a parameter recipe that silently assumed one rate would break the day the rate changes — this section shows every threshold moves *predictably* with `f`, so the recipe transfers. -**Result: the same wall-clock delay weighs more at a faster rate — everything else follows.** Because the load is `ρ = f·D_vis` (blocks produced per visibility delay, [§3.3](#s3-3)), a **faster** block rate makes the *same* wall-clock delay heavier (`fig6`, left): a fixed 8-s delay needs U = 1 at 30 s/20 s blocks but **U = 2 at 15 s and 10 s blocks**. Predicted `U_min = ⌈ρ⌉` vs. the measured smallest U reaching the 0.98 recovery bar (0.98 of the true value 1.0 — slot-counting removed the old `c(f)` ceiling; this sweep tested only **U ≤ 2**, so `>2` means U = 2 was still insufficient — consistent with a larger prediction): +**Result: the same wall-clock delay weighs more at a faster rate — everything else follows.** Because the load is `ρ = f·D_vis` (blocks produced per visibility delay, [§3.3](#s3-3)), a **faster** block rate makes the *same* wall-clock delay heavier (`fig6`, left): a fixed 8-s delay needs U = 1 at 30 s/20 s blocks but **U = 2 at 15 s and 10 s blocks**. Predicted `U_min = ⌈ρ⌉` vs. the measured smallest U reaching the 0.98 recovery bar (0.98 of the true value 1.0 — slot-counting removed the old `c(f)` ceiling; the sweep tested only **U ≤ 2**): -| delay (s) | 30 s (`⌈ρ⌉`/emp) | 20 s | 15 s | 10 s | +| propagation delay (s) | block interval 30 s | 20 s | 15 s | 10 s | |---|---|---|---|---| | 8 | 1 / 1 | 1 / 1 | 2 / 2 | 2 / 2 | | 16 | 1 / **2** | 2 / 2 | 2 / 2 | 3 / >2 | | 32 | 2 / **>2** | 3 / >2 | 4 / >2 | 6 / >2 | +*each cell = predicted `⌈ρ⌉` / smallest measured U reaching the 0.98 recovery bar; `>2` = U = 2 still insufficient (sweep capped at U ≤ 2).* + `⌈ρ⌉` matches in every fully-resolved cell **except two boundary cells** (one near-integer, one censored at U ≤ 2) — and error bars (standard error over replicates) show the two boundary cells are not alike: delay 16 / 30 s (`ρ = 0.96`) fails at U = 1 with `0.962 ± 0.006`, a **robust 3σ** under-shoot that genuinely needs U = 2; and delay 32 / 30 s (`ρ = 1.76`) reaches only `0.973 ± 0.002` at U = 2, a **4σ** shortfall — U = 2 genuinely fails there (matching the table's `>2`). This is why the `U = ⌈ρ⌉ + 1` margin exists and why boundary pass/fail calls must carry error bars. Every other `>2` cell is consistent with the larger `⌈ρ⌉` (the sweep only tested U ≤ 2). Three `f`-effects, all consistent with [§4](#s4) (plus one null result): - **recovery stays at 1.0** at every rate — slot-counting removes the `c(f)` dependence the block count had (the multi-winner rate `c(f)` = 1.017 → 1.054 from 30 → 10 s no longer appears in the estimate); - **`U_min` grows ∝ f** (same delay, faster rate ⇒ more uncles); @@ -260,7 +264,7 @@ Let `f` = block rate (blocks/slot; block interval `1/f` slots = seconds), and fo | 2 | load (orphans / block) | `ρ = f · D_vis` | governs U (fig6 collapse at ρ≈1) | | 3 | fully-recovered accuracy | `D̂/D = 1` (slot-counting, [§2.1](#s2-1)) | exact at equilibrium; deployed value ≈ `f/f_p` ≈ 1.01 from on-chain `f`-rounding only ([Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA)) | | 4 | accuracy, orphan-loss factor (U=0) | `D̂/D = ln(1−f)/ln(1−f/q_eff)` = `expected_ratio(f, q_eff)`, where the **effective density** `q_eff ≤ 1` is the fraction of active slots that are *counted* (canonical + recovered-uncle slots) | tight in the **orphan-loss regime** `q_eff < 1` (RMS 2.3e−4 vs the sim's `q_eff`, U=0 sweep); it *saturates at 1* as `q_eff → 1`, so the fully-recovered accuracy is **1.0 (eq 3)** — slot-counting counts each occupied slot once, so there is no multi-winner ceiling above it | -| 4′ | accuracy, no uncles (closed-form stand-in) | `D̂/D(U=0) ≈ 1 / (1 + a·ρ)`, `a ≈ 2.0` | `a = 2.01` fit, ρ ≳ 0.2 (RMS 0.056, ~240× coarser than eq. 4); worsens with N; ≈ 1 for direct gossip | +| 4′ | accuracy, no uncles (closed-form stand-in) | `D̂/D(U=0) ≈ 1 / (1 + a·ρ)`, `a ≈ 2` | `a ≈ 2` fit over the N = 1 000, U = 0 blend cells of `blend-hops-delay` + `rho-boundary` + `fullscale-small` (per-run best fits a = 1.4–2.2, pooled a = 1.8), ρ ≳ 0.2 (RMS ≈ 0.07 at `a = 2`, ~250× coarser than eq. 4); worsens with N; ≈ 1 for direct gossip | | 5 | **uncle cap** | necessary `U ≥ ⌈ρ⌉` (U<ρ **never** recovers); recommend `U = ⌈ρ⌉ + 1` | `⌈ρ⌉` matches emp. within ±1 — under-shoots just below integer ρ | | 6 | **uncle window** | `W_min ≈ 7/f` (≈ 200 slots @ f=1/30); margin `≈ 10/f` | ~const in delay/U; → ~10/f near uncle capacity | @@ -274,10 +278,12 @@ Inputs: f (block rate), propagation profile (hops, δ_max, ℓ_mean), deploym budget, cut propagation delay (fewer hops / less blending) — no window fixes U<ρ. Prefer to keep ρ < 1 with margin regardless: ρ > 1 is both the chronic under-count regime and the cheap grinding lever (§6.2–§6.3). -4. Uncle cap: if ρ ≪ 1 (direct gossip): U = 1 suffices (U=0 already ≈ 0.999) +4. Uncle cap: if ρ ≪ 1 (direct gossip): U = 1 suffices (U=0 alone already ≈ 0.97) else: U = ⌈ρ⌉ + 1 # recommended; ⌈ρ⌉ is the tight minimum, occasionally # short by one just below an integer ρ -5. Uncle window: W = ⌈10/f⌉ slots # ≥ 7/f floor; set by block SPACING, not by the delay +5. Uncle window: W = ⌈10/f⌉ slots # ≥ 7/f floor; set by block SPACING, not by the delay. + # Near the load boundary ρ ≈ 1, widen to 15–20/f (450–600 @ f=1/30) + # as a cheap alternative to the +1 uncle slot (§3.4, §8.1 row 3). 6. Expected accuracy: with U D̂/D → 1.0 (bounded by 1; spec 10^-3 f-rounding would add ~1%, App. A) without ≈ 1/(1+2ρ) for ρ ≳ 0.2, ≈ 1 for ρ ≪ 1 (direct gossip) 7. Security k: set by finality; TSI's per-node agreement held at k=2160, expected any k (§3.1) @@ -288,7 +294,7 @@ Inputs: f (block rate), propagation profile (hops, δ_max, ℓ_mean), deploym - *Blend (primary), 3 hops, δ_max = 8 s, f = 1/30.* `D_vis ≈ 3·4 + 4·1.2 ≈ 17` → `ρ ≈ 0.56`. Tight `⌈ρ⌉ = 1` (empirically suffices, [§3.5](#s3-5)); **recommended `U = 2`** (margin); `W = 300`. - *Same Blend at f = 1/10 (10 s blocks).* `ρ = 17/10 ≈ 1.7`. Tight `⌈ρ⌉ = 2` (needed, [§3.6](#s3-6)); **recommended `U = 3`**; `W = 10/f = 100`. -- *Direct global gossip (contrast), f = 1/30.* `D_vis = ℓ_mean ≈ 1.2` → `ρ ≈ 0.04`. Forks negligible: `U = 1` (U = 0 already gives `D̂/D ≈ 0.999`, well below where eq. 4′ applies); `W = 10/f = 300`. → the Cryptarchia defaults. +- *Direct global gossip (contrast), f = 1/30.* `D_vis = ℓ_mean ≈ 1.2` → `ρ ≈ 0.04`. Forks nearly negligible: `U = 1` (U = 0 alone already reaches `D̂/D ≈ 0.97` at degree 6 / `0.93` at degree 4, [§3.3](#s3-3) — well below where eq. 4′ applies; one uncle closes the last few percent to `1.000 ± 0.001`); `W = 10/f = 300`. → the Cryptarchia defaults (`W = 300` is the spec window `w_u`; the spec's `MAX_UNCLES = 4` sits well above the single uncle slot this regime needs). --- @@ -299,7 +305,7 @@ Inputs: f (block rate), propagation profile (hops, δ_max, ℓ_mean), deploym Read this before using the numbers: the regime they hold in, and the margins that absorb what they do not. - **Regime of exactness.** [§1](tsi-report-1-overview-and-recommendations.md#s1)–[§5](#s5) are for honest nodes with deterministic latency (`jitter = 0`), the regime in which the windowed/pruned engine is bit-exact; [§6](tsi-report-3-robustness-and-incentives.md#s6) tests the limits. **Open items:** sizing `W`/`U` so the emergent reference rate stays high under adversarial orphaning; the full multi-coalition (`K`-agent, [§6.9](tsi-report-3-robustness-and-incentives.md#s6-9)) selfish equilibrium (below-⅓ joint profitability unaddressed); per-node clock skew; and stochastic-jitter *parameter* tuning. -- **The `ρ ≈ 1` and `W ≈ 7/f` constants (load boundary, window floor) are semi-empirical** — the *functional forms* follow from the orphan-queueing mechanism, the constants are fitted (`a = 2.01`; `U = ⌈ρ⌉` within ±1). For production use the margined rules `U = ⌈ρ⌉ + 1` and `W = 10/f`. +- **The `ρ ≈ 1` and `W ≈ 7/f` constants (load boundary, window floor) are semi-empirical** — the *functional forms* follow from the orphan-queueing mechanism, the constants are fitted (`a ≈ 2`, pinned only to ~1.8–2.2 by the sweep; `U = ⌈ρ⌉` within ±1). For production use the margined rules `U = ⌈ρ⌉ + 1` and `W = 10/f`. - **N-scaling.** The U = 0 under-count worsens slowly with N (0.739 → 0.635 over N = 1k → 10k); the recovery thresholds for `U`/`W` are essentially N-invariant ([§3.4](#s3-4)). Size `D_vis`/`ρ` (and add margin to U) for the largest expected deployment; eq. 4′ itself is an N ≈ 1 000 fit. - **The residual ~1 %.** Slot-counting lands the equilibrium at exactly `D` ([§2.1](#s2-1)); the *only* systematic offset left is the on-chain integer rounding of `f` (`f_p = ⌊f·1000⌋/1000`, the `fixed_point` switch), which leaves the deployed estimate ≈ `f/f_p ≈ 1.01` high — common to every node (fairness untouched), an absolute ~1 % under-delivery of win probability, removed by carrying `f` at higher precision. **No correction exists in the specs today** ([Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA); [§8](tsi-report-1-overview-and-recommendations.md#s8) carries the precision bump as a recommendation). - **W and U are coupled but not fungible:** you cannot buy below the `~7/f` window floor with any number of uncles, and you cannot buy below `U = ⌈ρ⌉` with any window — though right at the boundary `ρ ≈ 1`, extra window (15–20/f) absorbs the fluctuation bursts that would otherwise need the `+1` uncle ([§3.4](#s3-4), fig25). diff --git a/reports/tsi/tsi-report-3-robustness-and-incentives.md b/reports/tsi/tsi-report-3-robustness-and-incentives.md index 1880305..9f34f60 100644 --- a/reports/tsi/tsi-report-3-robustness-and-incentives.md +++ b/reports/tsi/tsi-report-3-robustness-and-incentives.md @@ -1,6 +1,6 @@ # Total-Stake-Inference parameter selection — Robustness and incentives -*Per-node network simulation of Cryptarchia Total Stake Inference (TSI). Simulator: `tsi-sim-pernode`. All runs at the true security parameter **k = 2160** unless noted; latency is in slots and **1 slot = 1 s**.* +*Per-node network simulation of Cryptarchia Total Stake Inference (TSI). Simulator: `tsi-sim-pernode`. All runs at the true security parameter **k = 2160** and block rate **`f` = 1/30** (one block per 30 slots; [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)) unless noted; latency is in slots and **1 slot = 1 s**.* *[Part 1 — Overview & recommendations](tsi-report-1-overview-and-recommendations.md) · [Part 2 — Accuracy & design](tsi-report-2-accuracy-and-design.md) · [Part 3 — Robustness & incentives](tsi-report-3-robustness-and-incentives.md) · [Part 4 — Reproducibility & appendices](tsi-report-4-reproducibility-and-appendices.md) · [Index](README.md)* @@ -11,7 +11,7 @@ ## 6. Robustness beyond the honest, deterministic regime -[§1](tsi-report-1-overview-and-recommendations.md#s1)–[§5](tsi-report-2-accuracy-and-design.md#s5) characterise an honest, jitter-free regime, in which the two headline claims (one global estimate `D̂`; uncle cap `U` = the load `⌈ρ⌉` suffices) cannot fail by construction. Nine studies test those limits, forming one arc from network noise to a full adversary and its incentives: +[§1](tsi-report-1-overview-and-recommendations.md#s1)–[§5](tsi-report-2-accuracy-and-design.md#s5) characterise an honest, jitter-free regime, in which the two headline claims (one global estimate `D̂`; uncle cap `U` = the load `⌈ρ⌉` suffices, where the **load** `ρ = f·D_vis` is the number of blocks the network produces per block-visibility delay `D_vis` — [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)) cannot fail by construction. Eleven studies test those limits, forming one arc from network noise to a full adversary and its incentives, then out to the chain structure the estimate rides on and the wall-clock cadence it runs at: - **[§6.1](#s6-1)** consensus survives jitter (positive result). - **[§6.2](#s6-2)** the estimator is a load-feedback loop, bistable near `ρ≈1` in a fitted static map — a caveat, not reached in the full dynamics. @@ -20,38 +20,44 @@ - **[§6.5](#s6-5)** dynamic withhold-rejoin grinding — unprofitable, non-persistent. - **[§6.6](#s6-6)** selfish / private-chain withholding — the one profitable lever (above the classic stake threshold, quantified with the optimal-strategy MDP); uncle-*counting* still restores the estimate. - **[§6.7](#s6-7)** block/uncle *rewards* — robustly compensate honest orphans and disincentivise hiding, but a *voluntary* reward can backfire on selfish mining. -- **[§6.8](#s6-8)** a *soft* (reward-weighted) inclusion rule — the fork-safe choice (a validity rule cannot prove which forks a producer saw). The emergent reference rate stays high (honest blocks reference the published orphans), so the backfire mostly vanishes; the residual is set by `W`/visibility. +- **[§6.8](#s6-8)** a *soft* (reward-weighted) inclusion rule — the fork-safe choice (a validity rule cannot prove which forks a producer saw). The emergent reference rate stays high (honest blocks reference the published orphans), so the backfire mostly vanishes; the residual is set by the uncle window `W` (how far back a block may reach to reference an orphan; recommended 300 slots = 10/f, [§3.4](tsi-report-2-accuracy-and-design.md#s3-4)) and visibility. - **[§6.9](#s6-9)** multiple coalitions and bribery — the abstention commons is bounded and structure-independent; multi-coalition *selfish* mining is flagged, not solved. +- **[§6.10](#s6-10)** fork rate and reorg depth — uncles and `ρ < 1` keep reorganisations shallow and keep even a 30 % coalition below the effective-majority cliff. +- **[§6.11](#s6-11)** organic stake churn against the ~7.5-day epoch cadence — tracked with a one-epoch lag; a bounded rate wobble, never a consensus or accuracy failure. The recurring theme: the same uncle references that fix the honest under-count ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)) are also the adversarial safeguard — and *rewarding* them (softly) makes the safeguard incentive-compatible without a fork risk. ### 6.1 Consensus survives network jitter — not a determinism artifact -Adding random per-delivery arrival noise changes nothing: consensus stays exact. This needed testing because `range_ratio ≡ 0` in [§3.1](tsi-report-2-accuracy-and-design.md#s3-1) is exact by construction *only* at `jitter = 0`. Re-running in the simulator's guaranteed-exact mode (the full arrival matrix, with the windowed/pruning speed-ups disabled) with per-(block,node) arrival jitter across the full grid — `jitter_mean ∈ {0, 0.1, 0.3, 1, 3}` slots (the 0 cell is the exact baseline) × {regular, blend} × N ∈ {1 000, 2 000}, 10 replicates each — leaves **`range_ratio = 0 ± 0` and `agreement_window = 1.000` in every one of the 200 cells**, and the mean accuracy stays at 1.0 throughout (0.97–1.02 across cells at every jitter level) — jitter costs nothing in accuracy either. The only metric that moves is *current-tip* agreement, degrading monotonically (worst cell ≈ 0.98 → 0.86 as jitter grows to 3 slots): +Adding random per-delivery arrival noise changes nothing: consensus stays exact. This needed testing because `range_ratio ≡ 0` in [§3.1](tsi-report-2-accuracy-and-design.md#s3-1) is exact by construction *only* at `jitter = 0`. Re-running in the simulator's guaranteed-exact mode (the full arrival matrix, with the windowed/pruning speed-ups disabled) with per-(block,node) arrival jitter across the full grid — `jitter_mean ∈ {0, 0.1, 0.3, 1, 3}` slots (the 0 cell is the exact baseline) × both transports of [§2](tsi-report-2-accuracy-and-design.md#s2) — `regular` (plain direct gossip, sub-slot links, forks rare) and `blend` (the Blend mix cascade, whole-second per-hop blending delay — the deployment target) — × N ∈ {1 000, 2 000}, 10 replicates each — leaves **`range_ratio = 0 ± 0` and `agreement_window = 1.000` in all 200 runs (20 grid cells × 10 replicates)**, and the mean accuracy stays at 1.0 throughout (0.97–1.02 per run, 0.996–1.005 per replicate-averaged cell, at every jitter level; the few per-run values above 1 are per-epoch sampling noise around the `D̂/D ≤ 1` bound — [§2.2](tsi-report-2-accuracy-and-design.md#s2-2)) — jitter costs nothing in accuracy either. The only metric that moves is *current-tip* agreement, degrading monotonically (worst run ≈ 0.98 → 0.86, worst cell ≈ 0.99 → 0.94, as jitter grows to 3 slots): | `jitter_mean` (slots) | 0 | 0.1 | 0.3 | 1.0 | 3.0 | |---|---|---|---|---|---| -| `range_ratio` (max over cells) | 0 | 0 | 0 | 0 | 0 | +| `range_ratio` (max over runs) | 0 | 0 | 0 | 0 | 0 | | `agreement_window` (min) | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | -| mean `D̂/D` (range over cells) | 0.974–1.017 | 0.977–1.015 | 0.987–1.014 | 0.983–1.017 | 0.979–1.022 | -| `agreement_tip` (worst cell) | 0.977 | 0.957 | 0.945 | 0.928 | 0.859 | +| mean `D̂/D` (range over runs) | 0.974–1.017 | 0.977–1.015 | 0.987–1.014 | 0.983–1.017 | 0.979–1.022 | +| `agreement_tip` (worst run) | 0.977 | 0.957 | 0.945 | 0.928 | 0.859 | -Jitter feeds exactly the tip-level churn that [§3.1](tsi-report-2-accuracy-and-design.md#s3-1) showed never reaches the finalized density window. The reason is structural: the density window sits a full epoch length `E` (slots) past finality, so every block has reached every node by measurement time regardless of jitter, and all nodes still compute an identical `D̂`. The "one global `D̂`" claim therefore holds off the `jitter = 0` axis. *(Per-node clock skew — a whole-timeline shift of a node's slot clock, which unlike per-arrival jitter shifts a node's measurement-window bounds — was tested directly: a skew of up to ±20 slots moves each node's occupied-slot count by at most the one or two blocks in the shifted window edge, an inter-node spread of `≤ 1/m` ≈ `2·skew/T`. At the production window (`T ≈ 4×10⁵` slots) that is `< 10⁻⁴` — bounded and negligible, but, unlike jitter's exact 0, not identically zero. So bounded clock skew is a small quantifiable consensus cost, not a break.)* +Jitter feeds exactly the tip-level churn that [§3.1](tsi-report-2-accuracy-and-design.md#s3-1) showed never reaches the finalized density window. The reason is structural: the density window opens a full epoch back (`E = 10·⌊k/f⌋` slots) and *closes* `E − T = 4·⌊k/f⌋` slots before the chain is snapshotted for measurement — 259 200 slots ≈ 8 640 blocks ≈ 4k at k = 2160, f = 1/30, i.e. ~3k blocks deeper than `k`-finality — so every block has reached every node by measurement time regardless of jitter, and all nodes still compute an identical `D̂`. The "one global `D̂`" claim therefore holds off the `jitter = 0` axis. + +**Clock skew: bounded, but not identically zero.** A whole-timeline shift of a node's slot clock — unlike per-arrival jitter, it shifts the node's measurement-window bounds — was tested directly (its own generator, `scripts/clock_skew.py`, [§9](tsi-report-4-reproducibility-and-appendices.md#s9)). A skew of up to ±20 slots moves each node's occupied-slot count by at most the one or two blocks in the shifted window edge, an inter-node spread of at most `max(1/m, 2·skew/T)`, where `m = f·T` is the window's occupied-slot count — the discrete one-block floor `1/m` dominates for `skew < 1/(2f)`, and the measured spread is indeed a flat `1/m` at every skew from 1 to 20 slots. At the production window (`T = 6·⌊k/f⌋ = 388 800` slots, so `m = f·T = 12 960`) both terms are `≈ 1×10⁻⁴` — bounded and negligible, but, unlike jitter's exact 0, not identically zero. So bounded clock skew is a small quantifiable consensus cost, not a break ([§8.3](tsi-report-1-overview-and-recommendations.md#s8-3) item 6). ### 6.2 The estimator is a load-feedback loop, bistable near ρ≈1 in theory (`fig7`) The worry: the estimator feeds back on itself — a low estimate makes the lottery easier, more blocks collide, fewer get counted, and the estimate drops further. Could that spiral? The answer: only in a fitted static model, right at the load boundary `ρ ≈ 1`; the simulated network never reaches the spiral, but the boundary is real and is why we provision `ρ < 1` with margin. -Because the controller drives the *counted* density to `f`, the realised proposal rate is `f/r` (`r` = the recovered accuracy `D̂/D`; under-recovery means `r < 1`), so the realised load is `ρ_eff = ρ/r > ρ` whenever the estimate is under-recovered — this single effect explains both the U=0 finite-size drift and the near-integer `⌈ρ⌉` under-shoots. Fitting the effective counted density `q_eff` ([§4](tsi-report-2-accuracy-and-design.md#s4), eq. 4) as `q_eff ≈ 1/(1 + 0.71·ρ_eff)` and solving the self-consistent fixed point `r = ln(1−f)/ln(1−f/q_eff(ρ/r))` gives a single stable branch for `ρ ≲ 0.9` that **folds toward a collapsed low branch near `ρ ≈ 1`** — the map is bistable at the recipe's own operating boundary. So the honest-regime "`U = ⌈ρ⌉` suffices" line, computed on the high branch, is an upper edge, not a safe interior; the `+1` margin partly absorbs the `ρ_eff > ρ` gap. *Caveat:* this bistability is a property of the *fitted static* `q_eff(ρ)` map; the full per-node dynamics do **not** reach the fold — no simulated schedule flips to the collapsed branch ([§6.3](#s6-3)(i)) and a withhold pulse always recovers ([§6.5](#s6-5)(iv)). So the fold is a warning about *provisioning* margin, not an observed dynamical trap. +Because the controller drives the *counted* density to the target block rate `f` (blocks per slot; `f = 1/30`, one block every 30 slots = 30 s — defined in the [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) symbol table, and swept in [§3.6](tsi-report-2-accuracy-and-design.md#s3-6)), the realised proposal rate is `f/r` (`r` = the recovered accuracy `D̂/D`; under-recovery means `r < 1`), so the realised load is `ρ_eff = ρ/r > ρ` whenever the estimate is under-recovered — this single effect explains both the U=0 finite-size drift and the near-integer `⌈ρ⌉` under-shoots. Fitting the effective counted density `q_eff` ([§4](tsi-report-2-accuracy-and-design.md#s4), eq. 4) as `q_eff ≈ 1/(1 + 0.71·ρ_eff)` and solving the self-consistent fixed point `r = ln(1−f)/ln(1−f/q_eff(ρ/r))` gives a single reachable stable branch that **folds into a collapsed low branch at `ρ ≈ 1.08`** — the map is bistable at the recipe's own operating boundary. (`fig7`'s shaded band opens earlier, at `ρ ≈ 0.66`: that is where the unstable middle root rises above the low-`r` seed of the branch scan, so from `ρ ≈ 0.66` up a sufficiently deflated start already falls into the collapse basin, even though the upper branch itself survives to the fold.) So the honest-regime "`U = ⌈ρ⌉` suffices" line, computed on the high branch, is an upper edge, not a safe interior; the `+1` margin partly absorbs the `ρ_eff > ρ` gap. *Caveat:* this bistability is a property of the *fitted static* `q_eff(ρ)` map; the full per-node dynamics do **not** reach the fold — no simulated schedule flips to the collapsed branch ([§6.3](#s6-3)(i)) and a withhold pulse always recovers ([§6.5](#s6-5)(iv)). So the fold is a warning about *provisioning* margin, not an observed dynamical trap. -![Fig 7 — the estimator's self-consistent fixed point: a single stable branch for ρ≲0.9 folds toward a collapsed low branch near ρ≈1 in the fitted static map.](report-figures/fig7_feedback_bistability.png) +![Fig 7 — the estimator's self-consistent fixed point: the upper stable branch folds into a collapsed low branch at ρ≈1.08 in the fitted static map; the shaded band from ρ≈0.66 marks where a deflated start already falls into the collapse basin.](report-figures/fig7_feedback_bistability.png) + +*Figure note: the grey dotted line labelled "ceiling c(f)" (≈ 1.017) in the right panel is a leftover from the superseded block-counting rule and does **not** apply to any result in this report — under the corrected occupied-slot count the equilibrium `D̂/D` is bounded by 1 ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2), [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA)). It is a reference annotation only; neither plotted branch approaches it, so the fold result is unaffected.* ### 6.3 Grinding by uncle suppression is real but bounded, and scales with load (`fig8`) -The uncle mechanism is the attack surface: `D̂` is the denominator of the win probability `φ(f, w/D̂)` (`w` = the node's stake), so an adversary that references **no** uncles in its blocks starves the density count, deflates `D̂`, and inflates everyone's win rate — a grinding payoff. We added this to the engine (`adversary_frac`, a coalition holding a stake fraction `β_adv` that suppresses uncle refs; written `α` in the selfish-mining sections [§6.6](#s6-6)–[§6.8](#s6-8), and distinct from the TSI learning rate `β` of [§6.5](#s6-5)) and swept it × load (U = 2, N = 1 000): +The uncle mechanism is the attack surface: `D̂` is the denominator of the win probability `φ(f, w/D̂)` (`w` = the node's stake), so an adversary that references **no** uncles in its blocks starves the density count, deflates `D̂`, and inflates everyone's win rate — a grinding payoff. We added this to the engine (`adversary_frac`, a coalition holding a stake fraction `β_adv` that suppresses uncle refs; written `α` in the selfish-mining sections [§6.6](#s6-6)–[§6.8](#s6-8), and distinct from the TSI learning rate `β` of [§6.5](#s6-5)) and swept it × load (U = 2, N = 1 000; the table's β_adv cells are `D̂/D` under suppression, and **grinding gain** is the coalition's win-rate multiplier `1/(D̂/D)` — its lottery odds scale as `1/D̂` — reported at β_adv = 0.5): | load `ρ` | β_adv = 0.1 | 0.3 | 0.5 | grinding gain @ 0.5 | |---|---|---|---|---| @@ -59,14 +65,14 @@ The uncle mechanism is the attack surface: `D̂` is the denominator of the win p | 0.96 (boundary) | 0.996 | 0.949 | 0.876 | 1.14× | | 1.36 (U-limited) | 0.993 | 0.898 | **0.700** | **1.43×** | -Three findings: (i) the deflation is **smooth and monotone in `β_adv` — no catastrophic branch-flip** up to 50 % stake, so the [§6.2](#s6-2) bistability is not reached in this range (the fitted `q_eff` over-states the fold); (ii) at the honest operating load `ρ < 1` the attack is **weak** (honest blocks backfill the suppressed references within the window `W`), biting only in the U-limited `ρ > 1` regime; (iii) therefore **provisioning `U`/`W` to keep the operating point at `ρ < 1` with margin is *also* the adversarial safeguard** — operating at `ρ > 1` is doubly bad (honest under-recovery *and* a cheap grinding lever). *Precondition:* a counted uncle must be a real VRF (verifiable-random-function) lottery winner for its slot — the proof makes fabricating a win cryptographically impossible; modelled here, and it must be enforced on-chain. Block *withholding* — the stronger lever flagged here — is examined next in [§6.4](#s6-4). +Three findings: (i) the deflation is **smooth and monotone in `β_adv` — no catastrophic branch-flip** up to 50 % stake, so the [§6.2](#s6-2) bistability is not reached in this range (the fitted `q_eff` over-states the fold); (ii) at the honest operating load `ρ < 1` the attack is **weak** (honest blocks backfill the suppressed references within the window `W`), biting only in the U-limited `ρ > 1` regime; (iii) therefore **provisioning `U`/`W` to keep the operating point at `ρ < 1` with margin is *also* the adversarial safeguard** — operating at `ρ > 1` is doubly bad (honest under-recovery *and* a cheap grinding lever). *Precondition:* a counted uncle must be a real lottery winner for its slot — the spec's ZK Proof-of-Leadership makes fabricating a win cryptographically impossible, and this is already enforced on-chain; modelled here. Block *withholding* — the stronger lever flagged here — is examined next in [§6.4](#s6-4). ![Fig 8 — uncle-suppression grinding: D̂ deflation is smooth and monotone in the adversary stake, weak at ρ<1 and biting only in the U-limited ρ>1 regime.](report-figures/fig8_adversary.png) ### 6.4 Block withholding deflates `D̂` to ≈(1−β_adv), but measures reduced *active* stake (`fig9`) -Uncle suppression is a *reference-level* attack (the adversary publishes blocks but starves the density count). The stronger lever is **withholding**: the coalition wins its slots but never publishes, so its blocks never arrive at any honest node (arrival set past the epoch horizon `E`, so never received), are never adopted, and never counted. We added `adversary_strategy ∈ {suppress, withhold}` and re-ran the β_adv sweep on both topologies (N = 400, k = 256, U = 2, exact oracle): +Uncle suppression is a *reference-level* attack (the adversary publishes blocks but starves the density count). The stronger lever is **withholding**: the coalition wins its slots but never publishes, so its blocks never arrive at any honest node (arrival set past the epoch horizon `E`, so never received), are never adopted, and never counted. We added `adversary_strategy ∈ {suppress, withhold}` and re-ran the β_adv sweep on both transports (`regular` / `blend`, [§2](tsi-report-2-accuracy-and-design.md#s2)) (N = 400, k = 256, U = 2, exact oracle): | β_adv | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | vs. suppress @ 0.5 | |---|---|---|---|---|---|---| @@ -75,7 +81,7 @@ Uncle suppression is a *reference-level* attack (the adversary publishes blocks | suppress, regular | 1.000 | 1.000 | 0.999 | 0.996 | 0.999 | flat ≈ 1.0 | | suppress, blend | 1.001 | 0.997 | 0.996 | 0.995 | 0.992 | ≈ 1.0 | -Three findings: (i) withholding tracks the **active-stake line `D̂/D ≈ (1−β_adv)`** (grey dotted in `fig9`), sitting slightly below it, and is **largely topology-independent** — regular and blend deflate together — because the mechanism removes stake from the *count*, not from the propagation graph; suppression, by contrast, does essentially nothing on the well-connected regular graph and only bites weakly on blend at high load. (ii) The deflation **overshoots below (1−β_adv)** and does so more at large β_adv (at β = 0.5 the active line is 0.50; regular reaches 0.47, blend 0.41): once `D̂` collapses, the surviving honest nodes win *more* often at the deflated denominator, fork more, orphan more, and the density feeds back down — the [§6.2](#s6-2) load-feedback loop amplifying the withdrawal. (iii) Crucially, **this is not a measurement failure — it is TSI correctly reporting reduced active stake.** A coalition that withholds every block is indistinguishable from one that simply *went offline*; total-stake inference is defined over the stake that is *participating*, and (1−β_adv) is the right answer. +Three findings: (i) withholding tracks the **active-stake line `D̂/D ≈ (1−β_adv)`** (grey dotted in `fig9`), sitting slightly below it, and is **largely topology-independent** — regular and blend deflate together — because the mechanism removes stake from the *count*, not from the propagation graph; suppression, by contrast, does essentially nothing on the well-connected regular graph and only bites weakly on blend at high load. (ii) The deflation **overshoots slightly below (1−β_adv)** in every cell of the grid, but by a margin that shows **no resolvable trend in β_adv**: the shortfall is 0.038 / 0.076 / 0.065 / 0.037 / 0.028 on regular and 0.107 / 0.020 / 0.095 / 0.063 / 0.094 on blend at β_adv = 0.1 … 0.5, every cell within ≈ 2.6 SEM of the line at N = 400 × 16 replicates (regression of shortfall on β_adv: p = 0.53 regular, p = 0.90 blend). A plausible mechanism — once `D̂` falls, the surviving honest nodes win *more* often at the deflated denominator, fork more, orphan more, and the density feeds back down, the [§6.2](#s6-2) load-feedback loop nudging the withdrawal — is consistent with the uniformly negative sign, but this grid does not resolve its β_adv dependence. (iii) Crucially, **this is not a measurement failure — it is TSI correctly reporting reduced active stake.** A coalition that withholds every block is indistinguishable from one that simply *went offline*; total-stake inference is defined over the stake that is *participating*, and (1−β_adv) is the right answer. *Methodological note.* The peering graph is drawn per trajectory from the config's full RNG key, so adversary-vs-honest cells use different graph samples — a replicate-averaged variance source, not a bias; the deflation is topology-independent, so the conclusion is unaffected. @@ -88,7 +94,7 @@ Withholding is also **self-punishing**: the adversary forfeits all block rewards The static withholder of [§6.4](#s6-4) pays a permanent price. The dynamic variant tries to *time* participation: **abstain to deflate `D̂`, then re-activate to mine at the depressed difficulty**. We added a schedule (`adversary_period`, `adversary_withhold_epochs`) that withholds the coalition for part of each cycle and lets it behave honestly the rest, and attributed each epoch's canonical blocks to the coalition (reward accounting). Four results settle the threat. -**(i) The estimator is a moving average (EMA) of active stake; its speed is the learning rate `β`, not `W` (`fig10`).** Substituting the equilibrium density `m/T ≈ f·S_t·D*/D̂` into the spec recursion `D̂ ← D̂·(1 − β(f − m/T)/f)` gives, to leading order, `D̂_{t+1} = (1−β)·D̂_t + β·S_t·D*` — an exponential moving average of the active-stake signal `S_t·D*` (`S_t` = active fraction that epoch, `D*` = the honest-equilibrium estimate, which slot-counting puts at exactly `D` ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)); the [§6.5](#s6-5)/[§6.6](#s6-6) ratios `D̂/D*` are therefore the same `D̂/D` used in [§3](tsi-report-2-accuracy-and-design.md#s3)) with time-constant `τ = −1/ln(1−β)` epochs (this `β` is the TSI learning rate, `constants.BETA_DEFAULT` — unrelated to the coalition stake `β_adv`). The sim matches this law to **RMS 0.016** across `β ∈ {0.25, 0.5, 1.0}`. At the deployed learning rate **`β = 1` the estimator tracks active stake with a one-epoch lag** (`τ→0`); a withhold cycle then draws a near-square-wave sawtooth between `D*` and `(1−β_adv)D*`. A natural expectation is that the *uncle window* `W` sets the response speed; in fact responsiveness is set by the TSI learning rate `β`, *not* `W` (which sets equilibrium *accuracy*, not *speed*). A slower `β` shrinks the peak swing for a fixed schedule (amplitude 0.35 → 0.13 as `β`: 1 → 0.25) but, per (iii), buys the adversary nothing. +**(i) The estimator is a moving average (EMA) of active stake; its speed is the learning rate `β`, not `W` (`fig10`).** Substituting the equilibrium density `m/T ≈ f·S_t·D*/D̂` into the spec recursion `D̂ ← D̂·(1 − β(f − m/T)/f)` gives, to leading order, `D̂_{t+1} = (1−β)·D̂_t + β·S_t·D*` — an exponential moving average of the active-stake signal `S_t·D*` (`D̂_{t+1}` is the estimate computed at the *end* of epoch `t`, from that same epoch's activity, and in force during epoch `t+1`; `fig10` indexes it by the epoch in which it is computed, so the overlay is contemporaneous with `S_t`. `S_t` = active fraction in epoch `t`, `D*` = the honest-equilibrium estimate, which slot-counting puts at exactly `D` ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)); the [§6.5](#s6-5)/[§6.6](#s6-6) ratios `D̂/D*` are therefore the same `D̂/D` used in [§3](tsi-report-2-accuracy-and-design.md#s3)) with time-constant `τ = −1/ln(1−β)` epochs (this `β` is the TSI learning rate, `constants.BETA_DEFAULT` — unrelated to the coalition stake `β_adv`). The sim matches this law to **RMS 0.016** across `β ∈ {0.25, 0.5, 1.0}`. At the deployed learning rate **`β = 1` the estimate equals the current epoch's active stake outright** (`τ→0`, `D̂_{t+1} = S_t·D*`), and the one-epoch lag lives in the *lottery*, which spends the following epoch using it ([§6.11](#s6-11)); a withhold cycle then draws a near-square-wave sawtooth between `D*` and `(1−β_adv)D*`. A natural expectation is that the *uncle window* `W` sets the response speed; in fact responsiveness is set by the TSI learning rate `β`, *not* `W` (which sets equilibrium *accuracy*, not *speed*). A slower `β` shrinks the peak swing for a fixed schedule (amplitude 0.35 → 0.13 as `β`: 1 → 0.25) but, per (iii), buys the adversary nothing. ![Fig 10 — D̂ is an EMA of active stake; the withhold sawtooth's depth and speed are set by the learning rate β, matched by the EMA law (RMS 0.016).](report-figures/fig10_sawtooth.png) @@ -98,13 +104,13 @@ The static withholder of [§6.4](#s6-4) pays a permanent price. The dynamic vari |---|---|---|---|---|---|---|---|---| | reward / stake | 1.00 | 0.95 | 0.81 | 0.74 | 0.68 | 0.41 | 0.31 | 0.00 | -The curve is essentially **the same for `β = 0.5` and `β = 1.0`** — profitability is independent of estimator speed — and stays `< 1` for every minority coalition (`β_adv = 0.1 … 0.4` at the alternating schedule give 0.56 … 0.73). This is the [§6.4](#s6-4) subsidy made dynamic: the coalition **forfeits whole epochs** to depress a difficulty whose benefit — a higher win rate at lower `D̂` — accrues **equally to every honest node**, so its *relative* share never rises while it *alone* pays the forfeit. The reward-maximising schedule is `ψ = 0`: don't withhold. +The curve is **within `0.09` for `β = 0.5` and `β = 1.0`** at every duty — profitability is near-independent of estimator speed; the one visible gap is at the alternating `ψ = 0.5` (`0.59` at `β = 0.5` vs `0.68` at `β = 1.0`), where the period-2 schedule resonates with the fast estimator's one-epoch lag, and the two agree to `≤ 0.02` at every other `ψ` — and stays `< 1` for every minority coalition (`β_adv = 0.1 … 0.4` at the alternating schedule give 0.56 … 0.73). This is the [§6.4](#s6-4) subsidy made dynamic: the coalition **forfeits whole epochs** to depress a difficulty whose benefit — a higher win rate at lower `D̂` — accrues **equally to every honest node**, so its *relative* share never rises while it *alone* pays the forfeit. The reward-maximising schedule is `ψ = 0`: don't withhold. -**(iii) As a pure griefing lever it is bounded and linearly costly (`fig11`, right).** If the adversary abandons profit and only wants to distort `D̂`, the leaky-integrator form of (i) gives the mean deflation exactly: **`1 − ⟨D̂/D*⟩ = β_adv·ψ`** (bounded by `β_adv`, maximal at the static `ψ = 1`), cross-checked analytically and in sim. It costs the coalition `≈ ψ` of its *own* reward, so distortion is only a fraction `β_adv` of what the attacker forfeits — the distortion-vs-forfeit locus sits **below the 1:1 line** and a slower `β` does not lift it. There is **no super-linear amplification** in any regime; the one place the distortion-per-unit-*network*-reward-forfeited exceeds 1 is a bounded `≤ 2×` constant, and only for a `≈ 50 %` coalition under an *aggressive* estimator (`β ≥ 1`, rejoin overshoot) — a protocol-chosen gain, not an adversary lever. For minority coalitions it never exceeds the forfeit. +**(iii) As a pure griefing lever it is bounded and linearly costly (`fig11`, right).** If the adversary abandons profit and only wants to distort `D̂`, the leaky-integrator form of (i) gives the mean deflation exactly: **`1 − ⟨D̂/D*⟩ = β_adv·ψ`** (bounded by `β_adv`, maximal at the static `ψ = 1`), cross-checked analytically and in sim. It costs the coalition `≈ ψ` of its *own* reward, so distortion is only a fraction `β_adv` of what the attacker forfeits — the distortion-vs-forfeit locus sits **below the 1:1 line** and a slower `β` does not lift it. There is **no super-linear amplification** in any regime. Per unit of the *coalition's own* forfeited reward — the measure `fig11`(right) plots — the distortion is `0.30 – 0.63` across the duty sweep and `0.11 – 0.75` across `β_adv = 0.1 … 0.4`, always **below** 1:1. Normalised instead per unit of ***network*** reward forfeited (`β_adv·(1 − reward/stake)`), the ratio sits modestly above 1 across the **whole** tested grid — `1.14, 1.14, 1.67, 1.88` at `β_adv = 0.1, 0.2, 0.3, 0.4` (`β = 1`, `ψ = 0.5`), and `1.00 – 2.08` over `ψ` at `β_adv = 0.3` for **both** `β = 0.5` and `β = 1` — i.e. it is a small `≈ 2×` constant arising from rejoin overshoot, a protocol-chosen estimator gain rather than an adversary lever, not a regime the attacker can enter by growing. (Largest coalition simulated here is `β_adv = 0.4`; no `β_adv = 0.5` dynamic cell was run. The static `ψ = 1` grid of [§6.4](#s6-4), which does reach `β_adv = 0.5`, gives the same ratio *decreasing* with stake: `2.07 → 1.19` on blend and `1.38 → 1.06` on regular over `β_adv = 0.1 → 0.5`.) ![Fig 11 — dynamic withholding is unprofitable at every withhold duty (left); as a pure griefing lever the distortion is bounded and sub-linear in the reward forfeited (right).](report-figures/fig11_profitability.png) -**(iv) No self-sustaining collapse — the pulse is a pure transient (`fig12`).** The most worrying possibility is a withhold *pulse* that kicks the [§6.2](#s6-2) load-feedback loop across its fold into a *persistent* deflation that outlives the attacker. It does not: a 4–5-epoch pulse followed by honest behaviour returns `D̂` to the load-determined honest equilibrium at **every** operating point and **every** learning rate tested (`β = 0.25, 0.5, 1.0`). Where `D̂` sits low afterwards (0.21, 0.02 at `ρ ≫ 1`) that is the **chronic `ρ > 1` under-count of [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) / [§6.3](#s6-3) — a provisioning failure, not the adversary's doing** (the pulse-free honest run sits at the identical level). The per-node dynamics have a unique attracting equilibrium per operating point; the [§6.2](#s6-2) bistability of the *fitted static* `q_eff(ρ)` map does not create a trapping basin in the full dynamics. +**(iv) No self-sustaining collapse — the pulse is a pure transient (`fig12`).** The most worrying possibility is a withhold *pulse* that kicks the [§6.2](#s6-2) load-feedback loop across its fold into a *persistent* deflation that outlives the attacker. It does not: a 4-epoch pulse followed by honest behaviour returns `D̂` to the load-determined honest equilibrium at **every** operating point and **every** learning rate tested (`β = 0.25, 0.5, 1.0`). Where `D̂` sits low afterwards (0.21, 0.02 at `ρ ≫ 1`) that is the **chronic `ρ > 1` under-count of [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) / [§6.3](#s6-3) — a provisioning failure, not the adversary's doing** (the pulse-free honest run sits at the identical level). The per-node dynamics have a unique attracting equilibrium per operating point; the [§6.2](#s6-2) bistability of the *fitted static* `q_eff(ρ)` map does not create a trapping basin in the full dynamics. ![Fig 12 — a withhold pulse (grey band) always recovers to the load-determined equilibrium; where D̂ stays low afterwards it is the chronic ρ>1 under-count, not the adversary's doing.](report-figures/fig12_tipping.png) @@ -137,7 +143,7 @@ The curve is essentially **the same for `β = 0.5` and `β = 1.0`** — profitab ### 6.7 Block/uncle rewards: robust for fairness and anti-hiding, but a *voluntary* reward can backfire on selfish mining (`fig14`, `fig15`) -Everything above measures *blocks*. Whether an attack **pays** depends on the reward schedule, which is a design choice. We add one as a configurable option (`selfish.RewardParams`): a block reward (`= 1`), an **uncle reward** `w_u` paid to the *producer* of an orphaned block that is referenced as an uncle, and a **nephew reward** `w_n` paid to the block that *references* it. The model has five knobs in total: `w_u`, `w_n`, the honest-orphan reference rate `p_ref` (defined below), the attacker's self-uncling rate `p_ref_adv` (= 1 for a rational attacker), and `adv_nephew` — the fraction of referenced honest orphans whose *nephew* reward the attacker's own canonical blocks capture (0 without a forced-inclusion mandate, since honest blocks do the referencing). Three effects, all adversarially analysed. +Everything above measures *blocks*. Whether an attack **pays** depends on the reward schedule, which is a design choice. We add one as a configurable option (`selfish.RewardParams`): a block reward (`= 1`), an **uncle reward** `w_u` (a reward weight — distinct from the uncle *window*, which this report calls `W`) paid to the *producer* of an orphaned block that is referenced as an uncle, and a **nephew reward** `w_n` paid to the block that *references* it. The model has five knobs in total: `w_u`, `w_n`, the honest-orphan reference rate `p_ref` (defined below), the attacker's self-uncling rate `p_ref_adv` (= 1 for a rational attacker), and `adv_nephew` — the fraction of referenced honest orphans whose *nephew* reward the attacker's own canonical blocks capture (0 without a forced-inclusion mandate, since honest blocks do the referencing). Three effects, all adversarially analysed. **(1) It compensates orphaned honest producers (fairness).** A block-only schedule pays an orphaned honest block **nothing** — the same "off-chain, uncounted" fate that drives both the [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) latency under-count and the losses a selfish attacker inflicts. Define the **reference rate** `p_ref` = the probability that an orphaned honest block is referenced as an uncle by some canonical block within `W`. An uncle reward `w_u` refunds the loss in proportion to `p_ref`: honest recovery of *mined* value rises with `w_u` toward `1.0` (e.g. in the α = 0.4 selfish race, `0.61 → 0.80 → 1.00` for `w_u = 0 → 0.5 → 1` at `p_ref = 1`; `fig15`, right, plots recovery vs `p_ref`). The same references that restore the TSI *density* ([§6.6](#s6-6), `D̂`) restore the *reward*. **This benefit is robust** because a genuine latency orphan is *published* and straddled by *honest* canonical blocks that reference it, so `p_ref ≈ 1` here — unlike the selfish case in (3), where the attacker owns the straddling blocks. @@ -196,20 +202,34 @@ Everything above assumed a single coalition; this section asks what changes when **What we measure.** The engine records, every epoch, the **fork rate** (share of produced blocks orphaned off the canonical chain) and the **max reorg depth** (the deepest orphan branch — the confirmed blocks a node adopting it would have to discard). For the adversarial case we assume a coalition holding **0 %, 10 %, 20 %, or 30 %** of stake running a **private-chain deepest-reorg strategy**: it mines a hidden chain and releases it to override the public chain by the largest margin it can (the standard longest-chain attack, tuned for depth rather than revenue). Its reorg-depth tail is the Nakamoto gambler's-ruin `P(depth ≥ d) = (α_eff/(1−α_eff))^d`, coupled to the parameters through the *effective* adversary share `α_eff = α/(α + (1−α)(1−o))`, where `o` is the honest fork rate — because orphaned honest blocks do not extend the public chain, so more honest forking hands the attacker more relative power. -**Result 1 — delay drives fork depth, and uncles keep it shallow** (`fig28`, honest lines). Even with no adversary, the honest max reorg depth grows with Blend delay (2 blocks at δ = 2 s → 4 at δ = 32 s with U = 2). Without uncles it is far worse: the deflated estimate ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)) makes the network over-produce blocks, which fork among themselves — honest max depth reaches **17** at δ = 32 s, U = 0, versus **4** at U = 2. So uncles reduce reorg depth twice over: by keeping the block rate at `f` (no overproduction) and by keeping the operating point recoverable. +**Result 1 — delay drives fork depth, and uncles keep it shallow** (`fig28`, honest lines). Even with no adversary, the honest max reorg depth grows with the Blend per-hop blending-delay bound `δ` (`δ_max` in [§3.3](tsi-report-2-accuracy-and-design.md#s3-3)) — the privacy knob of the Blend mix-network transport ([§2](tsi-report-2-accuracy-and-design.md#s2)), and the dominant term in the visibility delay that sets the load `ρ` (2 blocks at δ = 2 s → 4 at δ = 32 s with U = 2). Without uncles it is far worse: the deflated estimate ([§3.2](tsi-report-2-accuracy-and-design.md#s3-2)) makes the network over-produce blocks, which fork among themselves — honest max depth reaches **17** at δ = 32 s, U = 0, versus **4** at U = 2. So uncles reduce reorg depth twice over: by keeping the block rate at `f` (no overproduction) and by keeping the operating point recoverable. **Result 2 — adversary depth grows with stake and with forking, and crosses a cliff** (`fig27`, `fig28`). At the recommended operating point (ρ < 1, δ ≈ 8 s, U = 2, honest fork rate ≈ 0.35) a 10 % coalition needs depth ~4 to reach 0.1 % probability, 20 % needs ~8, 30 % needs ~17 — reorgs of a handful of blocks. But heavier delay raises the honest fork rate, and at **δ = 32 s with 30 % stake the effective share `α_eff` crosses 0.5** — reorgs become **unbounded**: fork-induced orphaning has amplified a minority into an effective majority. Keeping ρ < 1 (few honest forks) keeps even a 30 % adversary bounded and shallow. -**Result 3 — a confirmation-depth rule for finality.** Turning the tail into a wait-time: at the recommended operating point (`o ≈ 0.35`), to hold `P(reorg ≥ d) < 10⁻³` a receiver waits **d ≈ 4 blocks (~2 min) against a 10 % adversary, 8 (~4 min) against 20 %, 17 (~8.5 min) against 30 %**; for a `10⁻⁶` guarantee, roughly double those (8 / 15 / 34 blocks). These are the confirmation depths for probabilistic settlement. The protocol's *deterministic* finality at `k = 2160` blocks is vastly deeper than any of these, so the finality-driven `k` ([§3.1](tsi-report-2-accuracy-and-design.md#s3-1)) is consistent with — and far more conservative than — the reorg tail; the confirmation-depth rule matters only for parties wanting faster-than-final soft settlement. - -**Design consequence.** The reorg-depth lever is the *operating point*, not the uncle cap: `U`/`W` fix what the estimate *counts*, but they reduce reorg depth only indirectly, by preventing the U = 0 overproduction spiral. Keep `ρ < 1` with margin — the same rule that keeps the estimate accurate ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)) and the grinding lever weak ([§6.3](#s6-3)) also keeps reorgs shallow and, crucially, keeps a large minority below the effective-majority cliff. The dependence on network size and degree is the [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) story read through the fork rate: a bigger or sparser network forks more, raising `α_eff`, so at the largest scales the shallow-reorg guarantee leans on the same `degree ≥ 6` recommendation that keeps `ρ` bounded (fork rate ≈ 0.35 at N = 1 000 degree 6, rising with N and falling with degree; `scripts/reorg_depth.py --measure-scale`). - -**Modelling note.** The private-chain race is a global-chain model like [§6.6](#s6-6)'s selfish mining, coupled to the engine only through the honest fork rate `o`; the honest fork/depth statistics are measured directly in the per-node engine. One caveat on `o`: it is the fork rate measured with **no adversary present**, transplanted into `α_eff` as a proxy for the public chain's forking during the attack. A pure private-chain attacker withholds its blocks until the reveal, so while it mines, the public chain is essentially honest and the no-adversary `o` is a close and slightly *conservative* proxy — an attack that lowers public forking would lower `α_eff` and shrink the tail. An attack that instead deliberately raises public forking, e.g. by strategically releasing blocks to split honest miners, would raise the attack-conditioned `o` above the honest baseline and is not captured here; the single-coalition bound is best-case-for-the-defender in that respect, [§8.3](tsi-report-1-overview-and-recommendations.md#s8-3) item 9. - ![Fig 27 — deepest-reorg probability tail P(depth ≥ d) per adversary stake at the recommended operating point; closed-form (lines) with Monte-Carlo validation (squares). 0 % stake forces no reorg.](report-figures/fig27_reorg_tail.png) ![Fig 28 — reorg depth vs Blend delay: honest max depth (engine, U=0 overproduces vs U=2) and the adversarial 99.9-percentile depth per stake. Depth grows with delay and stake; at 30 % stake past ρ≈1 it becomes unbounded. Uncles and ρ<1 keep it shallow.](report-figures/fig28_reorg_depth_vs_delay.png) +**Result 3 — a confirmation-depth rule for finality.** Turning the tail into a wait-time: at the recommended operating point (`o ≈ 0.35`), to hold `P(reorg ≥ d) < 10⁻³` a receiver waits **d ≈ 4 blocks (~2 min) against a 10 % adversary, 8 (~4 min) against 20 %, 17 (~8.5 min) against 30 %**; for a `10⁻⁶` guarantee, roughly double those (8 / 15 / 34 blocks). These are the confirmation depths for probabilistic settlement. The protocol's *deterministic* finality at `k = 2160` blocks is vastly deeper than any of these, so the finality-driven `k` ([§3.1](tsi-report-2-accuracy-and-design.md#s3-1)) is consistent with — and far more conservative than — the reorg tail; the confirmation-depth rule matters only for parties wanting faster-than-final soft settlement. These 4/8/17 depths are the **N = 1 000, degree-6** point; the scale study below shows how they move with size and connectivity. + +**Scale (N × degree).** The honest fork rate `o`, and through it the reorg depths, rises with network size and falls with peering degree. The 99.9 % confirmation depths (blocks) against a 10/20/30 % adversary, measured over `N × degree` (`scripts/reorg_depth.py --measure-scale`, `runs/fork_rate_vs_scale.parquet`): + +| N | degree | fork rate `o` | d(10 %) | d(20 %) | d(30 %) | +|---|---|---|---|---|---| +| 1 000 | 4 | 0.369 | 4 | 8 | 18 | +| 1 000 | 6 | 0.350 | 4 | 8 | 17 | +| 1 000 | 8 | 0.339 | 4 | 8 | 16 | +| 4 000 | 6 | 0.365 | 4 | 8 | 18 | +| 16 000 | 4 | 0.423 | 5 | 9 | 24 | +| 16 000 | 6 | 0.359 | 4 | 8 | 18 | +| 16 000 | 8 | 0.361 | 4 | 8 | 18 | + +The 30 %-stake depth is the sensitive one: the recommended **`degree ≥ 6`** holds it at 17–18 blocks across N = 1 000 → 16 000, while a sparse degree-4 graph lets it climb to 24 at N = 16 000 — the same connectivity margin that keeps `ρ` bounded ([§3.7](tsi-report-2-accuracy-and-design.md#s3-7)) keeps the reorg tail shallow at scale. + +**Design consequence.** The reorg-depth lever is the *operating point*, not the uncle cap: `U`/`W` fix what the estimate *counts*, but they reduce reorg depth only indirectly, by preventing the U = 0 overproduction spiral. Keep `ρ < 1` with margin — the same rule that keeps the estimate accurate ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)) and the grinding lever weak ([§6.3](#s6-3)) also keeps reorgs shallow and, crucially, keeps a large minority below the effective-majority cliff. The dependence on network size and degree is the [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) story read through the fork rate: a bigger or sparser network forks more, raising `α_eff`, so at the largest scales the shallow-reorg guarantee leans on the same `degree ≥ 6` recommendation that keeps `ρ` bounded (quantified in the Scale table above). + +**Modelling note.** The private-chain race is a global-chain model like [§6.6](#s6-6)'s selfish mining, coupled to the engine only through the honest fork rate `o`; the honest fork/depth statistics are measured directly in the per-node engine. One caveat on `o`: it is the fork rate measured with **no adversary present**, transplanted into `α_eff` as a proxy for the public chain's forking during the attack. A pure private-chain attacker withholds its blocks until the reveal, so while it mines, the public chain is essentially honest and the no-adversary `o` is a close and slightly *conservative* proxy — an attack that lowers public forking would lower `α_eff` and shrink the tail. An attack that instead deliberately raises public forking, e.g. by strategically releasing blocks to split honest miners, would raise the attack-conditioned `o` above the honest baseline and is not captured here; the single-coalition bound is best-case-for-the-defender in that respect, [§8.3](tsi-report-1-overview-and-recommendations.md#s8-3) item 9. + ### 6.11 Organic stake churn and the wall-clock cadence @@ -217,7 +237,7 @@ Everything above assumed a single coalition; this section asks what changes when **Why it matters.** If active stake moves faster than the estimator tracks it, the realised block rate drifts off target (over-production when stake fell, under when it rose) exactly as the [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) deflation does — the honest analogue of the withholding lever ([§6.5](#s6-5)). -**Result: TSI tracks organic churn with a one-epoch lag, and consensus never breaks** (`fig29`). We drove the active honest stake through a 30 %-amplitude sine, a linear ramp, and a sudden step — each over a period of 4 epochs (≈ 30 days at the production cadence, i.e. a *monthly*-scale swing) — and measured `D̂` against the *current* active stake. The [§6.5](#s6-5) EMA law holds for honest churn as it did for adversarial: the measured estimate follows the active stake within the epoch it is measured, so `D̂/D_total` tracks the active-stake fraction (dashed, `fig29`) and the churn-corrected `D̂/D_active` stays near 1 (means: sine 1.001, step 1.003, ramp 1.002; worst replicate-averaged epoch ≈ 0.98, worst single replicate ≈ 0.93 in the transient). At the sudden step down, `D̂/D_total` settles onto the new active fraction the *same* epoch and the corrected accuracy never leaves ~1 — the one-epoch lag lives in the *lottery*, which spends the transition epoch using the previous epoch's (higher) `D̂` before catching up: a brief rate overshoot that heals in one epoch, not a dip in the estimate. `range_ratio ≡ 0` throughout — churn shifts the common estimate, it does not split it. In wall-clock terms the lag is ~one epoch ≈ 7.5 days, so a monthly participation swing (period ≈ 4 epochs) is tracked with roughly a quarter-cycle phase error and a bounded amplitude error, and slower drifts (quarterly staking growth) essentially exactly. A genuinely *sub-epoch* swing — daily or weekly, faster than the 7.5-day epoch and the 4.5-day window — is not tracked as a cycle at all: the once-per-epoch measurement averages it out into a small bounded rate wobble (the estimator's Nyquist limit). +**Result: TSI tracks organic churn with a one-epoch lag, and consensus never breaks** (`fig29`). We drove the active honest stake through a 30 %-amplitude sine, a linear ramp, and a sudden step — each over a period of 4 epochs (≈ 30 days at the production cadence, i.e. a *monthly*-scale swing) — and measured `D̂` against the *current* active stake. The [§6.5](#s6-5) EMA law holds for honest churn as it did for adversarial: the measured estimate follows the active stake within the epoch it is measured, so `D̂/D_total` tracks the active-stake fraction (dashed, `fig29`) and the churn-corrected `D̂/D_active` stays near 1 (means: sine 1.001, step 1.003, ramp 1.002; worst replicate-averaged epoch ≈ 0.98, worst single replicate ≈ 0.93 in the transient). At the sudden step down, `D̂/D_total` settles onto the new active fraction the *same* epoch and the corrected accuracy never leaves ~1 — the one-epoch lag lives in the *lottery*, which spends the transition epoch using the previous epoch's (higher) `D̂` before catching up: a brief rate overshoot that heals in one epoch, not a dip in the estimate. `range_ratio ≡ 0` throughout — churn shifts the common estimate, it does not split it. In wall-clock terms the lag is ~one epoch ≈ 7.5 days, so a monthly participation swing (period ≈ 4 epochs) is tracked with roughly a quarter-cycle phase error and a bounded amplitude error, and slower drifts (quarterly staking growth) essentially exactly. A genuinely *sub-epoch* swing — daily or weekly, faster than the 7.5-day epoch and the 4.5-day window — is *reasoned, not simulated*: the engine resolves churn only at epoch granularity (`_churn_active_fraction(config, epoch)`, one `inactive_mask` per epoch) and the sweep's fastest cycle is a 2-epoch ≈ 15-day period, so no run exercises it. By sampling, a once-per-epoch measurement cannot resolve a cycle shorter than two epochs, so such a swing should not be tracked as a cycle at all but averaged into a small bounded rate wobble (the estimator's Nyquist limit) — an argument, not a measurement. **Design consequence.** The estimator is fit for organic churn *because* `β = 1` ([§8](tsi-report-1-overview-and-recommendations.md#s8) row 5): a slower learning rate would lengthen the lag and let a monthly cycle bias the rate more. The residual is a bounded rate wobble (a few percent for a 30 % monthly swing), never a consensus or accuracy failure. A protocol needing to *track* faster-than-monthly stake dynamics as a cycle (rather than average them out) would want a shorter epoch (smaller `k/f`), trading finality depth for tracking speed — the one place the finality-driven `k` and the tracking cadence trade off. diff --git a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md index b247fa6..fa24591 100644 --- a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md +++ b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md @@ -11,42 +11,44 @@ ## 9. Reproducibility -Sweep studies are committed configs, run with `make ` (writes a dated `runs/` folder with results + figures); standalone studies are scripts. In section order: +Sweep studies are committed configs, run with `make ` (writes a dated `runs/` folder with results + figures); standalone studies are scripts. Throughout this part, `D` is the true active stake, `D̂` a node's TSI estimate of it, `D̂/D` the accuracy (1.0 = exact; [§2.2](tsi-report-2-accuracy-and-design.md#s2-2)), `f` the target block rate (`1/30` here) and `ρ = f·D_vis` the delay load ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)). In section order: + +*Symbols used in this table (defined in Parts 2–3): `D̂/D` = recovered estimate ÷ true total stake; `U` = per-block uncle cap; `W` = uncle window in slots ([§3.4](tsi-report-2-accuracy-and-design.md#s3-4)); `ℓ_mean` = mean gossip path latency between two nodes, `D_vis` = mean visibility delay `hops·δ_max/2 + (hops+1)·ℓ_mean`, `ρ` = load `f·D_vis` ([§3.3](tsi-report-2-accuracy-and-design.md#s3-3)); `p_ref` = the probability an orphaned honest block is referenced as an uncle within `W` ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)).* | study | config / script | § | |---|---|---| -| full-scale confirmation (N, uncle recovery) | `configs/fullscale.yaml` (as committed: `n_nodes: [5000, 10000]`; the N = 1 000/2 000 rows come from earlier runs of the same config with `n_nodes` edited) | 3.1, 3.2 | -| bootstrap at full scale (k = 2160, Blend, N = 1 000/5 000, U ∈ {0, 2}) | `scripts/bootstrap_dynamics.py` (`runs/bootstrap_fullscale`) | 3.2 | -| one-uncle breakdown (hops × delay, N = 1 000/2 000) | `configs/blend-hops-delay.yaml`; fig3 by `scripts/hops_delay_grid.py` | 3.3 | -| ρ-boundary deficit sweep (`1 − D̂/D` vs ρ per U; hops=3, N=1000, 20 reps, k=256) | `configs/rho-boundary.yaml`; fig26 by `scripts/rho_boundary_analysis.py` | 3.3 | -| relative stake vs delay (D̂/D vs D_vis, per U) | `scripts/stake_vs_delay.py` | 3.3 | -| uncle-window sufficiency (W × delay, N = 1 000/2 000) | `configs/uncle-window.yaml` | 3.4 | -| joint (W, U) region (N = 1 000/2 000) | `configs/window-uncles.yaml` | 3.5 | -| block rate | `configs/block-rate.yaml` | 3.6 | +| full-scale confirmation (N, uncle recovery) | `configs/fullscale.yaml` (as committed: `n_nodes: [5000, 10000]`; the N = 1 000/2 000 rows come from a dedicated committed config, `configs/fullscale-small.yaml` — a separate, coarser grid, not this config re-run with `n_nodes` edited) | [§3.1](tsi-report-2-accuracy-and-design.md#s3-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) | +| bootstrap at full scale (k = 2160, Blend, N = 1 000/5 000, U ∈ {0, 2}) | `scripts/bootstrap_dynamics.py` (`runs/bootstrap_fullscale`) | [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) | +| one-uncle breakdown (hops × delay, N = 1 000/2 000) | `configs/blend-hops-delay.yaml`; fig3 by `scripts/hops_delay_grid.py` | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) | +| ρ-boundary deficit sweep (`1 − D̂/D` vs ρ per U; hops=3, N=1000, 20 reps, k=256) | `configs/rho-boundary.yaml`; fig26 by `scripts/rho_boundary_analysis.py` | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) | +| relative stake vs delay (D̂/D vs D_vis, per U) | `scripts/stake_vs_delay.py` | [§3.3](tsi-report-2-accuracy-and-design.md#s3-3) | +| uncle-window sufficiency (W × delay, N = 1 000/2 000) | `configs/uncle-window.yaml` | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | +| joint (W, U) region (N = 1 000/2 000) | `configs/window-uncles.yaml` | [§3.5](tsi-report-2-accuracy-and-design.md#s3-5) | +| block rate | `configs/block-rate.yaml` | [§3.6](tsi-report-2-accuracy-and-design.md#s3-6) | | heterogeneous-start (no re-convergence; N = 400, k = 256) | `configs/default.yaml` (`init_dest: heterogeneous`, `init_spread: 0.5`) | [Appendix C](#sC) | -| N-scaling of the one-uncle boundary (N = 1k–32k, cases a/b; k = 256) | `configs/nscaling-{a,b}.yaml`, `configs/nscaling32-{a,b}.yaml`; analysis + figures by `scripts/nscaling_analysis.py` | 3.7 | -| exact large-N topology probe (`ℓ_mean` to N = 10⁶, degrees 4/6/8) | `scripts/topology_probe.py` (`runs/topology_probe.parquet`) | 3.7 | -| link-latency shape sensitivity (exp vs geo at equal mean) | `configs/expdist.yaml` (baseline cells: the nscaling-a run) | 2 | -| stake-tail sensitivity (Pareto 1.33 vs 1.16) | `configs/pareto133.yaml` (baseline cells: the nscaling-a run) | 2 | -| window sufficiency at scale + W-as-buffer (N = 1 000/10 000, W ≤ 600) | `configs/window-scale.yaml`; fig25 by `scripts/window_scale_analysis.py` | 3.4 | -| fork rate + reorg depth vs delay/adversary stake | `scripts/reorg_depth.py` (`--measure`; `--measure-scale` for fork rate vs N/degree; `src/tsi_sim/reorg.py`); fig27, fig28 | 6.10 | -| organic stake churn (sine/ramp/step) | `scripts/churn.py` (`churn_amp`/`churn_period`/`churn_mode` fields); fig29 | 6.11 | -| per-node clock skew (bounded consensus cost) | `scripts/clock_skew.py` (`clock_skew_max` field) | 6.1 | -| capstone: recommended config end-to-end + 30 % adversary | `scripts/capstone.py` (`runs/capstone.parquet`) | 8.4 | -| jitter / consensus | `jitter_mean` > 0 + `windowed_fork_choice: false` (exact oracle); data in `runs/jitter_grid/results.parquet` | 6.1 | -| load-feedback fixed point | analysis of the U=0 sweep + `theory.expected_ratio` | 6.2 | -| adversarial grinding (uncle suppression) | `scripts/adversary_grid.py` (`adversary_frac` + `adversary_strategy: suppress`); data in `runs/adversary_grid/suppress.parquet` | 6.3 | -| block withholding | `scripts/adversary_grid.py` (`adversary_strategy: withhold`); data in `runs/adversary_grid/withhold.parquet` | 6.4 | -| dynamic withhold-rejoin grinding | `scripts/dynamic_withhold.py` (`adversary_period`, `adversary_withhold_epochs`) | 6.5 | -| selfish / private-chain withholding | `scripts/selfish_mining.py` (`src/tsi_sim/selfish.py`) | 6.6 | -| optimal selfish (SSZ MDP) + uncle rewards | `scripts/selfish_rewards.py` (`src/tsi_sim/selfish_mdp.py`, `RewardParams`) | 6.6, 6.7 | -| soft uncle inclusion (reward share vs emergent `p_ref`) | `scripts/reward_mandate.py` | 6.8, 6.9 | +| N-scaling of the one-uncle boundary (N = 1k–32k, cases a/b; k = 256) | `configs/nscaling-{a,b}.yaml`, `configs/nscaling32-{a,b}.yaml`; analysis + figures by `scripts/nscaling_analysis.py` | [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) | +| exact large-N topology probe (`ℓ_mean` to N = 10⁶, degrees 4/6/8) | `scripts/topology_probe.py` (`runs/topology_probe.parquet`) | [§3.7](tsi-report-2-accuracy-and-design.md#s3-7) | +| link-latency shape sensitivity (exp vs geo at equal mean) | `configs/expdist.yaml` (baseline cells: the nscaling-a run) | [§2](tsi-report-2-accuracy-and-design.md#s2) | +| stake-tail sensitivity (Pareto 1.33 vs 1.16) | `configs/pareto133.yaml` (baseline cells: the nscaling-a run) | [§2](tsi-report-2-accuracy-and-design.md#s2) | +| window sufficiency at scale + W-as-buffer (N = 1 000/10 000, W ≤ 600) | `configs/window-scale.yaml`; fig25 by `scripts/window_scale_analysis.py` | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | +| fork rate + reorg depth vs delay/adversary stake | `scripts/reorg_depth.py` (`--measure`; `--measure-scale` for fork rate vs N/degree; `src/tsi_sim/reorg.py`); fig27, fig28 | [§6.10](tsi-report-3-robustness-and-incentives.md#s6-10) | +| organic stake churn (sine/ramp/step) | `scripts/churn.py` (`churn_amp`/`churn_period`/`churn_mode` fields); fig29 | [§6.11](tsi-report-3-robustness-and-incentives.md#s6-11) | +| per-node clock skew (bounded consensus cost) | `scripts/clock_skew.py` (`clock_skew_max` field) | [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1) | +| capstone: recommended config end-to-end + 30 % adversary | `scripts/capstone.py` (`runs/capstone.parquet`) | [§8.4](tsi-report-1-overview-and-recommendations.md#s8-4) | +| jitter / consensus | `jitter_mean` > 0 + `windowed_fork_choice: false` (exact oracle); data in `runs/jitter_grid/results.parquet` | [§6.1](tsi-report-3-robustness-and-incentives.md#s6-1) | +| load-feedback fixed point | analysis of the U=0 sweep + `theory.expected_ratio` | [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) | +| adversarial grinding (uncle suppression) | `scripts/adversary_grid.py` (`adversary_frac` + `adversary_strategy: suppress`); data in `runs/adversary_grid/suppress.parquet` | [§6.3](tsi-report-3-robustness-and-incentives.md#s6-3) | +| block withholding | `scripts/adversary_grid.py` (`adversary_strategy: withhold`); data in `runs/adversary_grid/withhold.parquet` | [§6.4](tsi-report-3-robustness-and-incentives.md#s6-4) | +| dynamic withhold-rejoin grinding | `scripts/dynamic_withhold.py` (`adversary_period`, `adversary_withhold_epochs`) | [§6.5](tsi-report-3-robustness-and-incentives.md#s6-5) | +| selfish / private-chain withholding | `scripts/selfish_mining.py` (`src/tsi_sim/selfish.py`) | [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6) | +| optimal selfish (SSZ MDP) + uncle rewards | `scripts/selfish_rewards.py` (`src/tsi_sim/selfish_mdp.py`, `RewardParams`) | [§6.6](tsi-report-3-robustness-and-incentives.md#s6-6), [§6.7](tsi-report-3-robustness-and-incentives.md#s6-7) | +| soft uncle inclusion (reward share vs emergent `p_ref`) | `scripts/reward_mandate.py` | [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8), [§6.9](tsi-report-3-robustness-and-incentives.md#s6-9) | | U = 0 fluctuation series (zero delay, k ∈ {256, 1024, 2160}) | `scripts/appendix_fluct.py --run` (`runs/fluctuation_u0.parquet`) | [Appendix B](#sB) | | CI smoke grid + analytic sanity checks | `configs/smoke.yaml`; `scripts/verify.py` (`make verify`) — validation only, no figures | — | All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. -Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` from the block-rate run via `figures_pernode.py`; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` from the N = 10 000 run); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). +Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` (block-rate `U_min` grid + ρ-collapse) rendered ad hoc from `runs/2026-07-24_043943_block-rate` with no committed generator; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` pool both sizes in that run, N = 5 000 and N = 10 000 — the generators filter on stake_dist/topology/degree/init_dest only, never on `n_nodes`); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). --- @@ -54,7 +56,7 @@ Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `fi ## Appendix A — The residual ~1 % offset: on-chain rounding of `f` -**The question.** With correct slot-counting ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) the recovered estimate settles at `D`. Why does the *deployed* estimator carry a small residual ~1 % above `D`, and how is it removed? +**The question.** With correct slot-counting ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) the recovered estimate `D̂` settles at the true active stake `D`. Why does the *deployed* estimator carry a small residual ~1 % above `D`, and how is it removed? **The multi-winner slot, counted once.** The lottery gives node `i` an independent win chance `φ = 1 − (1−f)^{w_i/D̂}` (`w_i` = node i's stake). At `D̂ = D` the probability a slot has *at least one* winner is `1 − ∏(1−φ_i) = 1 − (1−f)^{Σw_i/D} = f` — slots activate at exactly the target rate. A slot can have *several* winners (the expected count is `−ln(1−f) = f·c(f) > f`, so busy slots are ~1.7 % more blocks than slots), and the surplus co-winners are always orphaned — even at zero delay. TSI counts **occupied slots**, so it counts such a slot **once**: the co-winner adds no count whether it is canonical or a referenced uncle. Holding the occupied-slot density at `f` therefore settles the estimate at exactly `D`, with no `c(f)` ceiling. (Counting uncle *blocks* instead double-counts these co-winner slots and inflates the equilibrium to `c(f)·D ≈ 1.017·D`; that is the deployed-spec bug and fix — see [§2.1](tsi-report-2-accuracy-and-design.md#s2-1) and [§8.5](tsi-report-1-overview-and-recommendations.md#s8-5).) @@ -70,36 +72,36 @@ Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `fi **The question.** The equilibrium is bounded by 1 ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2)), but individual epochs read 1.003 or 0.994. How large is that per-epoch noise, what sets it, and does it bias any single accuracy number in this report? -**The answer up front.** The U = 0 estimate is an *unbiased but noisy* measurement: its delay-free equilibrium is exactly 1 ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2)) and its per-epoch spread is pure sampling noise of the finite measurement window — `σ ≈ √((1−f)/(f·T))`, about **±0.9 % at the production window** (k = 2160). To show this cleanly we simulate the **delay-free limit directly** (full mesh, zero latency — no orphan loss at all, so *only* the noise remains); a realistic sub-slot gossip series then confirms the same magnitude, and the delay progression (§B.3) shows how real orphan loss turns that noise one-sided, pinning the estimate **below** 1 — the bounded-by-1 deficit of [§3.2](tsi-report-2-accuracy-and-design.md#s3-2). Every number below is measured; nothing is asserted. +**The answer up front.** The U = 0 estimate is an *unbiased but noisy* measurement: its delay-free equilibrium is exactly 1 ([§2.2](tsi-report-2-accuracy-and-design.md#s2-2)) and its per-epoch spread is pure sampling noise of the finite measurement window — `σ ≈ √((1−f)/(f·T))`, about **±0.9 % at the production window** (k = 2160). To show this cleanly we simulate the **delay-free limit directly** (full mesh, zero latency — no orphan loss at all, so *only* the noise remains); a realistic sub-slot gossip series then confirms the same magnitude, and the delay progression ([§B.3](#sB-3)) shows how real orphan loss turns that noise one-sided, pinning the estimate **below** 1 — the bounded-by-1 deficit of [§3.2](tsi-report-2-accuracy-and-design.md#s3-2). Every number below is measured; nothing is asserted. ### B.1 The mechanism: a stochastic controller passes its measurement noise through -At U = 0 with negligible delay the counted density is the *active-slot* rate, which the lottery calibrates to exactly `f` at `D̂ = D` (the identity of A.1) — so the fixed point is exactly 1, with no ceiling. But the measured density `m/T` is a random variable: the window contains only `f·T` expected blocks, so one epoch's measurement carries relative noise `σ ≈ √((1−f)/(f·T))`. At the deployed learning rate `β = 1` the update `D̂ ← D̂·(1 − β(f − m/T)/f)` passes that noise straight into the estimate: each epoch's `D̂/D` is `≈ 1 + ε` with `ε` the window's sampling error. The estimate is therefore *expected* to read 1.003 or 0.994 in individual epochs — those are not anomalies but the noise floor itself. +At U = 0 with negligible delay the counted density is the *active-slot* rate, which the lottery calibrates to exactly `f` at `D̂ = D` (the multi-winner identity of [Appendix A](#sA)) — so the fixed point is exactly 1, with no ceiling. But the measured density `m/T` is a random variable: the window contains only `f·T` expected blocks, so one epoch's measurement carries relative noise `σ ≈ √((1−f)/(f·T))`. At the deployed learning rate `β = 1` the update `D̂ ← D̂·(1 − β(f − m/T)/f)` passes that noise straight into the estimate: each epoch's `D̂/D` is `≈ 1 + ε` with `ε` the window's sampling error. The estimate is therefore *expected* to read 1.003 or 0.994 in individual epochs — those are not anomalies but the noise floor itself. ### B.2 Measured: the ±0.9 % noise floor, shrinking as 1/√T A dedicated zero-delay series (full mesh, link latency `L = 0`, U = 0, equal stakes, 4 × 120 epochs per k) isolates the fluctuation with no orphan loss at all: -| k (window `T = 6⌊k/f⌋`) | mean `D̂/D` | per-epoch σ (measured) | σ theory | P(`D̂/D` > 1) | largest excursion | +| k (window `T = 6⌊k/f⌋`) | mean `D̂/D` | per-epoch σ (measured) | σ theory | P(`D̂/D` > 1) | largest excursion (448 epochs) | |---|---|---|---|---|---| -| 256 | 0.99914 | 0.0254 | 0.0251 | 0.50 | **1.066** | -| 1024 | 1.00079 | 0.0126 | 0.0125 | 0.54 | 1.035 | -| 2160 | 1.00006 | 0.0088 | 0.0086 | 0.53 | 1.024 | +| 256 | 0.99914 | 0.0254 | 0.0251 | 0.50 | **1.082** (3.3σ) | +| 1024 | 1.00079 | 0.0126 | 0.0125 | 0.54 | 1.049 (3.9σ) | +| 2160 | 1.00006 | 0.0088 | 0.0086 | 0.53 | 1.035 (4.1σ) | -The mean is pinned at 1 to within ±0.001 at every window size — the estimator is unbiased at the bound — while the spread follows the `1/√T` law to within a few percent. `figB1` shows the per-epoch trace at k = 2160 on a per-mil axis: the clean zero-delay series and the realistic 0.1-slot direct-gossip series wander together inside the predicted ±σ band. +The mean is pinned at 1 to within ±0.001 at every window size — the estimator is unbiased at the bound — while the spread follows the `1/√T` law to within a few percent. `figB1` shows the per-epoch trace at k = 2160 on a per-mil axis: the clean zero-delay series and the realistic 0.1-slot direct-gossip series (epochs 4–16, where the two overlap) both fluctuate about zero *on the scale of* the predicted ±σ_th band — 65 % of zero-delay epochs fall inside it, the ~68 % a ±1σ band should contain — with Gaussian tails out to ≈ 4σ (+35 per-mil). The band is the noise scale, not a bound. -![Fig B1 — per-epoch (D̂/D − 1) in per-mil at U=0, k=2160: the zero-delay and sub-slot-gossip series wander inside the ±σ_th = √((1−f)/fT) sampling-noise band around the ≤1 equilibrium.](report-figures/figB1_fluctuation_trace.png) +![Fig B1 — per-epoch (D̂/D − 1) in per-mil at U=0, k=2160: the zero-delay series (epochs 4–119) and the sub-slot-gossip series (epochs 4–16) fluctuate about zero on the scale of the ±σ_th = √((1−f)/fT) sampling-noise band — ~2/3 of epochs inside it, tails to ≈4σ — around the ≤1 equilibrium.](report-figures/figB1_fluctuation_trace.png) ### B.3 Delay converts the fluctuation into a one-sided under-count -The committed full-scale N = 1 000 (k = 2160) data shows how real delay changes the picture (`figB2`, middle): at 0.1-slot links the U = 0 estimate reads `1.0004 ± 0.0087` with `P(>1) = 50 %`; at 0.2 slots the mean slips to 0.997 and `P(>1)` to 39 %; by 0.5-slot links orphan loss dominates (mean 0.963, **never** above 1 in 300 epochs); and under Blend U = 0 sits far below (mean 0.74, maximum 0.997). So "fluctuates around 1" is the *delay-free limit* of the U = 0 estimator; in the deployment regime (Blend) the U = 0 estimate is one-sidedly low, and the fluctuation instead rides on the recovered value; blend at U = 1 crosses 1.0 in ~50 % of epochs, the same symmetric noise around the recovered fixed point. +The committed full-scale N = 1 000/2 000 (k = 2160) data shows how real delay changes the picture (`figB2`, middle): at 0.1-slot links the U = 0 estimate reads `0.9993 ± 0.0089` with `P(>1) = 52 %`; at 0.2 slots the mean slips to 0.9955 and `P(>1)` to 34 %; by 0.5-slot links orphan loss dominates (mean 0.962, **never** above 1 in the 136 tail epochs); and under Blend U = 0 sits far below (mean 0.726, maximum 0.993). So "fluctuates around 1" is the *delay-free limit* of the U = 0 estimator; in the deployment regime (Blend) the U = 0 estimate is one-sidedly low, and the fluctuation instead rides on the recovered value; blend at U = 1 crosses 1.0 in ~50 % of epochs, the same symmetric noise around the recovered fixed point. -**Delay also changes the *size* of the fluctuation — but not gradually** (`figB2`, right). Under direct gossip the per-epoch spread stays at the sampling floor at every link delay (σ = 0.007–0.009 from 0.1 to a full slot): mild orphan loss shifts the *mean*, not the noise. Under Blend at U = 0 the fluctuation **explodes to σ ≈ 0.14–0.15 — about 17× the floor**: with a third of blocks orphaning, the counted density is decided by fork races, and the [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) load feedback (a deflated `D̂` raises the raw proposal rate, which raises orphaning again) amplifies that race noise into ±14 % per-epoch swings. **A single uncle restores not just the mean but the noise floor itself**: at U = 1 the per-epoch σ returns to 0.009 in every cell, Blend included — the uncle mechanism stabilises the estimator's *variance* as well as its *bias*, a second, independent reason to provision `U` correctly. +**Delay also changes the *size* of the fluctuation — but not gradually** (`figB2`, right). Under direct gossip the per-epoch spread stays at the sampling floor at every link delay (σ = 0.008–0.010 from 0.1 to a full slot): mild orphan loss shifts the *mean*, not the noise. Under Blend at U = 0 the fluctuation **explodes to σ ≈ 0.15–0.16 — about 18× the floor**: with a third of blocks orphaning, the counted density is decided by fork races, and the [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) load feedback (a deflated `D̂` raises the raw proposal rate, which raises orphaning again) amplifies that race noise into ±15 % per-epoch swings. **A single uncle restores not just the mean but the noise floor itself**: at U = 1 the per-epoch σ returns to 0.009 in every cell, Blend included — the uncle mechanism stabilises the estimator's *variance* as well as its *bias*, a second, independent reason to provision `U` correctly. -![Fig B2 — left: the per-epoch deviation distribution shrinks as 1/√T (k = 256 → 2160, measured σ vs theory); middle: as link delay grows the U=0 mean drops below 1 and P(D̂/D > 1) collapses to zero — orphan loss is one-sided; right: per-epoch σ stays at the sampling floor under direct gossip but explodes ~17× under Blend at U=0, and one uncle restores the floor.](report-figures/figB2_fluctuation_stats.png) +![Fig B2 — left: the per-epoch deviation distribution shrinks as 1/√T (k = 256 → 2160, measured σ vs theory); middle: as link delay grows the U=0 mean drops below 1 and P(D̂/D > 1) collapses to zero — orphan loss is one-sided; right: per-epoch σ stays at the sampling floor under direct gossip but explodes ~18× under Blend at U=0, and one uncle restores the floor.](report-figures/figB2_fluctuation_stats.png) ### B.4 What precision is meaningful @@ -117,13 +119,13 @@ A reading like `1.001` is well inside one epoch's noise (±0.009 at k = 2160) ### C.1 Per-epoch traces at the largest scale -`fig17` shows the per-epoch picture **at the largest tested scale, N = 10 000** (30 epochs, 6 replicates): the per-node `D̂/D` spread (full range and interquartile range, top) sits at 0 for the whole run while node agreement on the finalized window prefix (bottom) stays at 1.000 — the consensus result holds unchanged from `N = 1 000` up to `N = 10 000`. +`fig17` shows the per-epoch picture **at the two largest tested scales pooled, N = 5 000 and N = 10 000** (the `fullscale` config sweeps both sizes; 6 replicates per cell, up to 30 epochs — early stopping thins the trace after ≈ epoch 24, so the last points rest on a handful of trajectories): the per-node `D̂/D` spread (full range and interquartile range, top) sits at 0 for the whole run while node agreement on the finalized window prefix (bottom) stays at 1.000 — the consensus result holds unchanged from `N = 1 000` up to `N = 10 000`. -![Fig 17 — at N=10000, per-node D̂/D spread stays ≡ 0 and window agreement ≡ 1.000 across all 30 epochs, even as current-tip agreement stays below 1.](report-figures/fig17_divergence.png) +![Fig 17 — pooled over N=5000 and N=10000, per-node D̂/D spread stays ≡ 0 and window agreement ≡ 1.000 at every epoch reached, even as current-tip agreement stays below 1.](report-figures/fig17_divergence.png) -The one metric that is *not* exactly 1 is **current-tip** agreement (`fig18`, also N = 10 000): nodes share the live tip most of the time (≈ 0.985–0.994 typical), dipping to ~0.985 in the worst cell — a small, transient tip churn that never reaches the deeply-buried density window, which is why `D̂` agreement is exact regardless. +The one metric that is *not* exactly 1 is **current-tip** agreement (`fig18`, same fullscale run — but its `U = 0` curves pool both sizes in that run, N = 5 000 and N = 10 000): nodes share the live tip most of the time (≈ 0.985–0.994 typical), dipping to ~0.985 in the worst plotted cell; restricted to N = 10 000 the same cells run 0.978–0.996 (worst 0.978 at degree 6, delay 1 s), and the worst tip cell at N = 10 000 over all `U` is 0.971 — a small, transient tip churn that never reaches the deeply-buried density window, which is why `D̂` agreement is exact regardless. -![Fig 18 — current-tip agreement at N=10000 is high but below 1 (≈ 0.985–0.994 typical, ~0.985 worst cell); the transient tip forking it measures never propagates into D̂.](report-figures/fig18_tip_agreement.png) +![Fig 18 — current-tip agreement (fullscale run, U=0, N=5000 and N=10000 pooled) is high but below 1 (≈ 0.985–0.994 typical, ~0.985 worst plotted cell; 0.978–0.996 restricted to N=10000); the transient tip forking it measures never propagates into D̂.](report-figures/fig18_tip_agreement.png) ### C.2 Consensus rests on common initialization — there is no active re-convergence diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/appendix_fluct.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/appendix_fluct.py index 75aff0d..9cabfb0 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/appendix_fluct.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/appendix_fluct.py @@ -131,7 +131,10 @@ def figs() -> None: # right: per-epoch sigma (within a trajectory) vs case, U=0 vs U=1 def per_epoch_sigma(s: pd.DataFrame) -> float: - return float(s.groupby(["degree", "replicate"]).mean_ratio.std().mean()) + # per-trajectory epoch std, then mean over trajectories. Group by n_nodes too: the + # fullscale-small run holds N=1000 and N=2000 at the same (degree, replicate), and + # pooling them would fold their between-N mean offset into the within-trajectory sigma. + return float(s.groupby(["degree", "n_nodes", "replicate"]).mean_ratio.std().mean()) cases: list[tuple[str, pd.DataFrame]] = [] for lat in (0.1, 0.2, 0.5, 1.0): @@ -153,7 +156,7 @@ def figs() -> None: ax3.set_yscale("log") ax3.set_xticks(x3, [c for c, _ in cases], rotation=20, ha="right", fontsize=8) ax3.set_ylabel(r"per-epoch $\sigma$ of $\hat D / D$") - ax3.set_title("Blend delay amplifies U = 0 noise ~17×;\none uncle restores the floor") + ax3.set_title("Blend delay amplifies U = 0 noise ~18×;\none uncle restores the floor") ax3.legend(fontsize=8) style.save(fig, FIGS / "figB2_fluctuation_stats", provenance="scripts/appendix_fluct.py") plt.close(fig) diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py index eb15948..09455af 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py @@ -51,8 +51,12 @@ def fig1(df: pd.DataFrame) -> None: gdfs = sorted(d.gdf.unique()) for i, gdf in enumerate(gdfs): for u, ls in ((2, "-"), (0, "--")): + # Both panels are indexed by the estimate that DROVE each epoch's production: the + # start-of-epoch estimate `mean_ratio_in` (block rate depends on it, and at epoch 0 it + # IS the genesis guess, matching the legend). Plotting end-of-epoch `mean_ratio` here + # would show the already-updated value at epoch 0 and offset the two panels by one epoch. s = (d[(d.gdf == gdf) & (d.u == u)] - .groupby("epoch").agg(rate=("n_blocks", "mean"), ratio=("mean_ratio", "mean"))) + .groupby("epoch").agg(rate=("n_blocks", "mean"), ratio=("mean_ratio_in", "mean"))) rate = s.rate / (10 * int(2160 / F)) # blocks per slot ax1.plot(s.index, rate, ls, color=style.OKABE_ITO[i], lw=1.4, ms=3, marker="o" if u == 2 else None, diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py index 9739056..c293eb1 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py @@ -21,14 +21,31 @@ import pandas as pd sys.path.insert(0, str(Path(__file__).resolve().parents[1] / "src")) +from tsi_sim.config import SimConfig # noqa: E402 from tsi_sim.plotting import style # noqa: E402 +from tsi_sim.topology import build_path_latency # noqa: E402 HERE = Path(__file__).resolve().parent.parent RUNS = HERE / "runs" FIGS = HERE / "report-figures" -F = 1.0 / 30.0 -HOPS = 3 -LMEAN = 1.2 # degree-6, N=1000 geo graph (matches §4) + + +def graph_ell_mean(df: pd.DataFrame) -> float: + """``ell_mean`` — the mean shortest-path (gossip) latency of the run's OWN peering graph. + + Measured from the run's recorded ``(n_nodes, degree, link_latency_mean, link_latency_dist)`` + rather than hardcoded, so the rho axis stays correct if any of those change. It is a statistical + property of the random d-regular geo graph (seed-invariant to <1% at this N), so one + representative draw suffices. Post-processing only — this rebuilds the latency *graph* to read + off its mean, and never touches or re-runs the simulation. + """ + row = df.iloc[0] + cfg = SimConfig(n_nodes=int(row.n_nodes), degree=int(row.degree), topology="blend", + link_latency_mean=float(row.link_latency_mean), + link_latency_dist=str(row.link_latency_dist), k=int(row.k)) + pl = build_path_latency(cfg, np.random.default_rng(0)) + n = pl.shape[0] + return float(pl[~np.eye(n, dtype=bool)].mean()) def load() -> pd.DataFrame: @@ -37,9 +54,19 @@ def load() -> pd.DataFrame: keys = ["blend_delay_max", "max_uncles", "replicate"] df["emax"] = df.groupby(keys).epoch.transform("max") tail = df[df.epoch >= df.emax // 2] - g = (tail.groupby(["blend_delay_max", "max_uncles"]) + # Per-trajectory tail mean FIRST, then mean + SEM ACROSS replicates. Pooling every + # (replicate x tail-epoch) row instead would treat correlated within-trajectory epochs as + # independent samples and understate the true replicate spread (by ~1.5x, up to ~3x). + per_rep = (tail.groupby(keys, as_index=False).mean_ratio.mean()) + g = (per_rep.groupby(["blend_delay_max", "max_uncles"]) .mean_ratio.agg(["mean", "sem"]).reset_index()) - g["rho"] = F * (HOPS * g.blend_delay_max / 2.0 + (HOPS + 1) * LMEAN) + # Derive the rho axis from the run itself — f, hops, and the *measured* ell_mean — not from + # hardcoded constants: rho = f*D_vis with D_vis = hops*delta_max/2 + (hops+1)*ell_mean. This + # only re-labels the x-axis from the existing simulation data; it never re-simulates. + f = float(df.f.iloc[0]) + hops = int(df.blend_hops.iloc[0]) + ell = graph_ell_mean(df) + g["rho"] = f * (hops * g.blend_delay_max / 2.0 + (hops + 1) * ell) g["deficit"] = 1.0 - g["mean"] return g @@ -48,13 +75,22 @@ def fig26(g: pd.DataFrame) -> None: import matplotlib.pyplot as plt style.apply_style() fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9.6, 4.2)) + floor = 3e-4 for i, U in enumerate((0, 1, 2, 3)): s = g[g.max_uncles == U].sort_values("rho") c = style.OKABE_ITO[i] - # left: deficit (floored at a small positive value for the log axis) - d = np.clip(s.deficit.values, 3e-4, None) - ax1.plot(s.rho, d, "-o", ms=4, color=c, label=f"U = {U}") - # right: accuracy, capped at 1.0 + # left: deficit on a log axis. A cell counts as a RESOLVED positive deficit only if it + # is both positive and above its own 2*SEM noise level; unresolved cells (at/below noise, + # or slightly negative because D̂/D sits a hair above 1 from sampling noise) are clamped to + # the axis floor and drawn HOLLOW, so a point on the floor cannot be misread as a measured + # deficit. A faint line joins the series for legibility. + rho = s.rho.values + d = np.clip(s.deficit.values, floor, None) + resolved = (s.deficit.values > floor) & (s.deficit.values > 2.0 * s["sem"].values) + ax1.plot(rho, d, "-", lw=0.8, color=c, alpha=0.5, zorder=0) + ax1.plot(rho[resolved], d[resolved], "o", ms=4, color=c, label=f"U = {U}") + ax1.plot(rho[~resolved], d[~resolved], "o", ms=4, mfc="none", mec=c) + # right: accuracy, capped at 1.0, with the across-replicate SEM ax2.errorbar(s.rho, s["mean"], yerr=s["sem"], fmt="-o", ms=4, capsize=2, color=c, label=f"U = {U}") ax1.set_yscale("log") diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/stake_vs_delay.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/stake_vs_delay.py index 2594e08..52fef7c 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/stake_vs_delay.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/stake_vs_delay.py @@ -1,9 +1,9 @@ """Relative stake estimate vs network delay (fig16). Shows the report's central relationship: the recovered *relative stake* ``D̂/D`` as a function of the -mean block-visibility delay ``D_vis`` (seconds), one curve per uncle cap ``U``. Accuracy holds near -the ceiling ``c(f)`` while the load ``ρ = f·D_vis`` stays below ``⌈U⌉``, then collapses — so larger -delay needs more uncles. Blend transport, f = 1/30 (30 s blocks); delay swept via the +mean block-visibility delay ``D_vis`` (seconds), one curve per uncle cap ``U``. Accuracy holds at +the 1.0 exact-recovery bound while the load ``ρ = f·D_vis`` stays below ``⌈U⌉``, then collapses — so +larger delay needs more uncles. Blend transport, f = 1/30 (30 s blocks); delay swept via the per-hop blending budget ``blend_delay_max``. Run: python scripts/stake_vs_delay.py (writes runs/stake_vs_delay.parquet + fig16) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py index 349d179..76edec3 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py @@ -115,8 +115,10 @@ class SimConfig: k: int = 64 # scaled by default; full scale = 2160 genesis_d_factor: float = 0.5 # genesis D = factor * true total stake epochs: int = 40 - # If True, mirror the spec's integer fixed-point f-truncation (f_p = int(f*1000)/1000), - # which the on-chain estimator uses; this reproduces its ~1% systematic overestimate. + # If True, quantise the target rate the way an on-chain integer estimator does: + # f_p = int(f*tsi.PRECISION)/tsi.PRECISION. With tsi.PRECISION = 1_000_000 (the report's + # recommended 10^-6 f-precision, §8) this gives f_p = 0.033333 and a negligible residual + # f/f_p < 1e-5 — not the ~1% overestimate the old 10^-3 truncation produced. # Default False keeps the analysis-faithful exact-f behaviour. fixed_point: bool = False # If True, count uncle references per BLOCK ID (the pre-fix behaviour, which double-counts @@ -139,9 +141,10 @@ class SimConfig: churn_amp: float = 0.0 churn_period: int = 4 churn_mode: ChurnMode = "sine" - # Per-node constant slot-clock offset (~Uniform(-clock_skew_max, +clock_skew_max) slots), - # applied to each node's measurement-window bounds — tests whether a whole-timeline clock shift - # (unlike per-arrival jitter) can split slot-occupancy at the window edges and break consensus. + # INERT: nothing reads this. The §6.1 clock-skew study is run stand-alone by + # scripts/clock_skew.py, which applies its own per-node offsets — not through this field. + # Retained only as a key() seed contributor for run-hash compatibility (like `per_node_dest`); + # leave at 0. clock_skew_max: int = 0 # Each node updates its OWN D_est from its OWN view — the point of this simulator, and the ONLY # mode implemented here (always True). The global-consensus-D_est baseline (per_node_dest=False) @@ -155,8 +158,9 @@ class SimConfig: init_spread: float = 0.0 # relative spread of heterogeneous initial D_est # --- performance --- - # >1 parallelises the per-slot lottery across slot-chunks (opt-in; must be pinned and - # recorded because it changes the RNG stream — see lottery.sample_wins_chunked). + # INERT: nothing reads this — `simulate_epoch` never calls `lottery.sample_wins_chunked`, + # so it has no modelled effect. Retained as a key() seed contributor for run-hash + # compatibility (like `per_node_dest` above); leave at 1. lottery_chunks: int = 1 # Windowed fork choice bounds the per-slot candidate scan to a horizon of the max path # latency (plus the fully-propagated best tip), turning O(n_blocks^2) into O(n_blocks*H). diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py index 4248413..9db0c57 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py @@ -13,7 +13,8 @@ The counted density ``m`` is SLOT-based (canonical slots + recovered uncle slots recovered orphan slots, window-prefix fingerprint) runs as one cached, C-speed routine over flat arrays. A pure-Python fallback keeps the package importable without numba. -Results are identical to the reference loop (``measure_reference``); see test_measure. +Results are identical to the naive per-node loop (``_reference`` in tests/test_measure.py; +see ``test_measure_matches_reference``). """ from __future__ import annotations @@ -35,7 +36,8 @@ except ImportError: # pragma: no cover - numba is an optional accelerator @dataclass class Measurement: - m: np.ndarray # (N,) per-node block count + m: np.ndarray # (N,) per-node counted density: canonical + recovered uncle SLOTS + # (per-block-id count only under legacy_block_count=True) q: np.ndarray # (N,) honest active-slot fraction q_eff: np.ndarray # (N,) uncle-recovered fraction orphan_rate: np.ndarray # (N,) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py index f9c6fb6..6d933ab 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py @@ -1,4 +1,4 @@ -"""Per-epoch per-node divergence rows and equilibrium summaries.""" +"""Per-epoch per-node divergence rows.""" from __future__ import annotations @@ -60,23 +60,3 @@ def divergence_row( p_ref=er.p_ref, ) return row - - -def equilibrium_stats(values: np.ndarray, burn_in: int) -> dict[str, float]: - """Mean/variance of ``values`` after ``burn_in`` epochs.""" - values = np.asarray(values, dtype=float) - if values.size == 0: - return {"mean": float("nan"), "var": float("nan"), "std": float("nan")} - tail = values[burn_in:] - if tail.size == 0: - tail = values[-1:] - return {"mean": float(np.mean(tail)), "var": float(np.var(tail)), "std": float(np.std(tail))} - - -def epochs_to_within(values: np.ndarray, target: float, eps: float) -> int: - """First epoch after which ``|values - target| <= eps`` holds for the rest.""" - within = np.abs(np.asarray(values, dtype=float) - target) <= eps - if within.size == 0: - return 0 - false_idx = np.flatnonzero(~within) - return int(false_idx[-1] + 1) if false_idx.size else 0 diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py index d2171fa..9f08222 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py @@ -13,9 +13,14 @@ import pandas as pd from . import style -CONFIG_COLS = ["n_nodes", "stake_dist", "topology", "degree", "link_latency_mean", - "blend_hops", "blend_delay_max", "latency", "max_uncles", - "uncle_strategy", "uncle_window", "init_dest", "k"] +# A trajectory's identity: every config axis a sweep can vary. Anything swept but ABSENT here is +# silently averaged into one cell — the block-rate sweep varies `f`, so it must be listed — so keep +# this exhaustive over the recorded config fields (see metrics._CONFIG_FIELDS). +CONFIG_COLS = ["n_nodes", "stake_dist", "pareto_shape", "topology", "degree", + "link_latency_mean", "link_latency_dist", "blend_hops", "blend_delay_max", + "latency", "max_uncles", "uncle_strategy", "uncle_window", + "init_dest", "init_spread", "genesis_d_factor", + "f", "beta", "k", "fixed_point", "legacy_block_count"] # Graph topologies (as opposed to the full_mesh baseline) and the dominant latency knob each # is plotted against: regular varies the per-link latency, blend varies the per-hop mix delay. diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/reorg.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/reorg.py index 3d3231e..a537084 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/reorg.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/reorg.py @@ -20,8 +20,11 @@ per-node loop. Two ingredients tie it to the protocol parameters: ``+1`` w.p. ``alpha_eff`` (adversary extends privately), ``-1`` w.p. ``1-alpha_eff`` (honest extends the public chain). Each excursion above 0 is one attack; the deepest reorg it can force is the maximum lead reached (release the private chain at its peak, displacing that many public - confirmations). The tail is the Nakamoto/Rosenfeld gambler's-ruin first passage - ``P(depth >= d) = (alpha_eff/(1-alpha_eff))**d`` for ``alpha_eff < 1/2``. + confirmations). ``P(depth >= d) = (alpha_eff/(1-alpha_eff))**d`` (``alpha_eff < 1/2``) is the + Nakamoto/Rosenfeld gambler's-ruin *catch-up* probability — the chance an adversary ``d`` blocks + behind ever draws level — an upper bound on that per-attack maximum, not its exact distribution + (which is smaller). ``fig27`` plots the occupancy Monte-Carlo; §6.10's 4/8/17 and 8/15/34 are the + engine's realised reorg depths. """ from __future__ import annotations diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py index 8250745..cb96976 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py @@ -19,13 +19,15 @@ def expected_ratio(f: float, q: ArrayLike) -> ArrayLike: def block_count_ceiling(f: float) -> float: - """Equilibrium ratio at *full* uncle recovery for the equal-stake limit. + """LEGACY-mode ceiling: the equilibrium ratio under ``legacy_block_count=True``. - TSI counts blocks (all lottery wins, rate ``-ln(1-f)`` per slot in the small-stake - limit), whereas ``f`` is the *active-slot* rate. So even with every orphan recovered the - estimate equilibrates at ``-ln(1-f)/f`` (~1.017 for f=1/30), not 1.0. This is a - deterministic overshoot floor, not noise; concentrated (Pareto) stake gives a smaller - value because of the concavity of ``phi``. + Applies only to the superseded per-*block* counting (``tsi.density_m(..., + legacy_block_count=True)``), which counted every lottery win (rate ``-ln(1-f)`` per slot + in the small-stake limit) while ``f`` is the *active-slot* rate. In that mode, even with + every orphan recovered the estimate equilibrated at ``-ln(1-f)/f`` (~1.017 for f=1/30) — + a deterministic overshoot, not noise; concentrated (Pareto) stake gave a smaller value + from the concavity of ``phi``. The default slot-counting engine has no such ceiling: the + equilibrium is bounded by 1 (report §2.1/§2.2). """ return -np.log(1.0 - f) / f From bd2ac7b7be2799ef64383d3df1e5861d0751bcab Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Tue, 4 Aug 2026 18:48:46 +0200 Subject: [PATCH 02/22] Countable uncle model: spec counting rules, sweeps, figures Implement the countable uncle model from the Cryptarchia spec's counting-only reference rules, and make it the simulator default. Counting rules (uncles.py, measure.py): - Only the first block of a fork (parent on the producer's chain) is referenceable and countable, which makes every reference verifiable from chain data alone. - The reference window is derived from a window-absorption parameter, w_u = W_abs/f slots (W_abs in expected block-intervals, default 10, bounded W_abs <= 0.6*k), replacing the free-standing uncle_window. - Selection skips slots already occupied on the producer's chain and takes at most one uncle per slot. - The measurement pass re-checks every rule per reference and tallies rejections as deep_ref_share. The pre-redesign model is preserved behind --old on tsi-sweep and tsi-verify. Its RNG key is byte-identical to the pre-uncle_model key, so --old bit-reproduces the historical runs. Supporting changes: uncle_model and window_absorption config surface with validation (config.py, constants.py); accuracy closed form over the effective q_u (theory.py); plumbing through tsi.py, epoch.py, sweep.py, blocktree.py, metrics.py, verify.py, figures_pernode.py. Studies and figures: - configs/countable-vs-old.yaml -- delay x U grid, run under both models on the same grid. - configs/absorption-window.yaml -- accuracy vs W_abs at U=1. - scripts/plot_countable_vs_old.py renders fig30-fig33 into reports/tsi/report-figures/. Tests: tests/test_countable_counting.py (7 cases) covering first-fork eligibility, derived-window bounds, occupied-slot exclusion, and per-reference re-checking; extensions to test_uncles.py, test_config.py, test_slot_counting.py. Full fast suite: 202 passed. Also adds CLAUDE.md (graphify project instructions) and ignores editor/local-agent state plus the vendored Equi-X benchmark clone. The reports/tsi/ prose describing this model is held back for a separate editorial pass. Co-Authored-By: Claude Opus 5 (1M context) --- .gitignore | 8 + CLAUDE.md | 9 + .../report-figures/fig30_countable_vs_old.png | Bin 0 -> 172481 bytes .../fig31_countable_prediction.png | Bin 0 -> 118785 bytes .../fig32_countable_recovery.png | Bin 0 -> 202799 bytes .../fig33_absorption_window.png | Bin 0 -> 148156 bytes .../simulators/tsi/tsi-sim-pernode/README.md | 14 +- .../configs/absorption-window.yaml | 26 +++ .../configs/countable-vs-old.yaml | 23 +++ .../scripts/plot_countable_vs_old.py | 169 ++++++++++++++++++ .../tsi-sim-pernode/src/tsi_sim/blocktree.py | 4 +- .../tsi/tsi-sim-pernode/src/tsi_sim/config.py | 76 +++++++- .../tsi-sim-pernode/src/tsi_sim/constants.py | 15 +- .../tsi/tsi-sim-pernode/src/tsi_sim/epoch.py | 10 +- .../tsi-sim-pernode/src/tsi_sim/measure.py | 94 ++++++++-- .../tsi-sim-pernode/src/tsi_sim/metrics.py | 4 +- .../src/tsi_sim/plotting/figures_pernode.py | 13 +- .../tsi/tsi-sim-pernode/src/tsi_sim/sweep.py | 13 +- .../tsi/tsi-sim-pernode/src/tsi_sim/theory.py | 24 +++ .../tsi/tsi-sim-pernode/src/tsi_sim/tsi.py | 41 ++++- .../tsi/tsi-sim-pernode/src/tsi_sim/uncles.py | 148 ++++++++++++--- .../tsi/tsi-sim-pernode/src/tsi_sim/verify.py | 13 +- .../tsi/tsi-sim-pernode/tests/test_config.py | 67 ++++++- .../tests/test_countable_counting.py | 84 +++++++++ .../tests/test_slot_counting.py | 20 ++- .../tsi/tsi-sim-pernode/tests/test_uncles.py | 90 +++++++++- 26 files changed, 888 insertions(+), 77 deletions(-) create mode 100644 CLAUDE.md create mode 100644 reports/tsi/report-figures/fig30_countable_vs_old.png create mode 100644 reports/tsi/report-figures/fig31_countable_prediction.png create mode 100644 reports/tsi/report-figures/fig32_countable_recovery.png create mode 100644 reports/tsi/report-figures/fig33_absorption_window.png create mode 100644 tools/simulators/tsi/tsi-sim-pernode/configs/absorption-window.yaml create mode 100644 tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml create mode 100644 tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py create mode 100644 tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py diff --git a/.gitignore b/.gitignore index 83972fa..559613b 100644 --- a/.gitignore +++ b/.gitignore @@ -216,3 +216,11 @@ __marimo__/ # Streamlit .streamlit/secrets.toml + +# Editor / local agent state +.obsidian/ +.claude/settings.json +.claude/settings.local.json + +# External upstream clones vendored for benchmarking (own .git, not our history) +tools/benchmarks/original/ diff --git a/CLAUDE.md b/CLAUDE.md new file mode 100644 index 0000000..417efeb --- /dev/null +++ b/CLAUDE.md @@ -0,0 +1,9 @@ +## graphify + +This project has a knowledge graph at graphify-out/ with god nodes, community structure, and cross-file relationships. + +Rules: +- For codebase questions, first run `graphify query ""` when graphify-out/graph.json exists. Use `graphify path "" ""` for relationships and `graphify explain ""` for focused concepts. 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      c75Z2BcWfi!RE@xoNqQA)gU(LZQ|^xLHbAzgA$wZI?thd zE5C}Q$ANIvMNTKnJE|Nr{GaV13d b=WmOK)-7H>Z}+)J_?OI$FJE99y2ShsYpuA- literal 0 HcmV?d00001 diff --git a/tools/simulators/tsi/tsi-sim-pernode/README.md b/tools/simulators/tsi/tsi-sim-pernode/README.md index d054f63..9acf057 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/README.md +++ b/tools/simulators/tsi/tsi-sim-pernode/README.md @@ -38,6 +38,16 @@ - **Per-node views:** one global block tree plus an `(N × n_blocks)` **arrival matrix** `A`; each node builds on / measures density over the blocks that have arrived at it. Uncle refs are **baked at production** from the producer's view (faithful — immutable once adopted). +- **Uncle model (`uncle_model`, CLI `--old`):** the default **countable** model implements the + spec's counting-only rules (cryptarchia-v1-protocol.md): only the **first block of a fork** + (parent on the producer's chain) is referenceable/countable, the window is **derived** as + `w_u = window_absorption / f` slots (`W` expected block-intervals, default `W = 10` → 300 + slots, bounded `W ≤ 0.6·k`), selection skips slots already occupied on the producer's chain + and picks one uncle per slot, and the measurement pass re-checks every rule per reference + (rejections tallied as `deep_ref_share`). Passing `--old` to `tsi-sweep`/`tsi-verify` runs + the pre-redesign model unchanged — window = `uncle_window` slots, any-depth orphans + referenceable, every baked reference counted — and **bit-reproduces historical runs** (the + old model's RNG key is byte-identical to the pre-`uncle_model` key). - **Metrics:** per-node `D_est` spread (`range`, `IQR`), canonical-chain **agreement** (window prefix vs current tip), mean accuracy, and — with `init_dest=heterogeneous` — transient re-convergence. @@ -145,6 +155,8 @@ src/tsi_sim/ constants config rng stake lottery topology blocktree(+build_tree uncles(+select_uncles_at_production) tsi(+update_D_vec) epoch engine metrics theory verify plotting/{style, figures_pernode, make_figures} configs/ smoke.yaml default.yaml fullscale.yaml + countable-vs-old.yaml absorption-window.yaml (countable-model studies) tests/ test_{pernode,config,rng,lottery,blocktree,uncles,tsi_counting,stake, - theory,latency,theory_convergence}.py + theory,latency,theory_convergence,countable_counting,...}.py +scripts/ plot_countable_vs_old.py (old-vs-countable comparison figures) ``` diff --git a/tools/simulators/tsi/tsi-sim-pernode/configs/absorption-window.yaml b/tools/simulators/tsi/tsi-sim-pernode/configs/absorption-window.yaml new file mode 100644 index 0000000..38b95e8 --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/configs/absorption-window.yaml @@ -0,0 +1,26 @@ +# Countable model: sweep the window absorption parameter W (w_u = W/f slots derived) at +# U=1 against the Blend mixing delay. The window-miss contribution to non-recovery is +# (1-f)^(W/f) ~ e^-W (theory.window_miss_prob): recovery should saturate within a few +# expected block-intervals, with the residual set by the delay (orphans spread wider than +# the window) and by the first-fork restriction. The countable counterpart of the old +# model's uncle-window.yaml (which swept uncle_window in raw slots; run that with --old). +# Latency is in SLOTS (1 slot = 1 s). +n_nodes: [1000] # network size +stake_dist: [pareto] # heavy-tailed (realistic) stake distribution +topology: [blend] # Blend mixnet (delay stresses the window) +degree: [6] # peering degree of the d-regular graph +link_latency_mean: [0.5] # natural geographic transport (sub-slot) +link_latency_dist: [geo] # real-world geographic band mixture +blend_hops: [3] # fixed hop count; delay is the swept knob +blend_delay_max: [8.0, 16.0, 32.0] # max per-relay mixing delay (slots) +window_absorption: [1, 2, 3, 5, 7, 10] # W: window in expected block-intervals +max_uncles: [1] # FIXED at one uncle (the question is about W) +uncle_strategy: [oldest] # spec selection: oldest-first fill +init_dest: [common] # per-node initial D_est from agreement +replicates: 5 # independent RNG replicates per grid cell +base: # per-run settings shared by every cell + k: 2160 # true security parameter + epochs: 20 # equilibrium within ~2 epochs; burn 50% + f: 0.03333333333333333 # slot activation coefficient (1/30) + genesis_d_factor: 0.5 # start near true stake (cheap epoch 0) + early_stop: true diff --git a/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml b/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml new file mode 100644 index 0000000..3bdd5d6 --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml @@ -0,0 +1,23 @@ +# Headline comparison for the countable uncle model (cryptarchia-v1-protocol.md counting +# rules) vs the old pre-redesign model: accuracy vs Blend mixing delay at U in {0,1,2,4}. +# Run TWICE — default (countable) and with --old — same grid; the countable run also +# yields deep_ref_share (the first-fork restriction's rejection rate) and q/q_eff for the +# q_u = q + (1-q) r theory overlay. Latency is in SLOTS (1 slot = 1 s). +n_nodes: [1000] # network size +stake_dist: [pareto] # heavy-tailed (realistic) stake distribution +topology: [blend] # Blend mixnet (the multi-slot fork regime) +degree: [6] # peering degree of the d-regular graph +link_latency_mean: [0.5] # natural geographic transport (sub-slot) +link_latency_dist: [geo] # real-world geographic band mixture +blend_hops: [3] # fixed hop count; delay is the swept knob +blend_delay_max: [4.0, 8.0, 16.0, 32.0] # max per-relay mixing delay (slots) +max_uncles: [0, 1, 2, 4] # U: 0 baseline, then the recovery levers +uncle_strategy: [oldest] # spec selection: oldest-first fill +init_dest: [common] # per-node initial D_est from agreement +replicates: 5 # independent RNG replicates per grid cell +base: # per-run settings shared by every cell + k: 2160 # true security parameter + epochs: 20 # equilibrium within ~2 epochs; burn 50% + f: 0.03333333333333333 # slot activation coefficient (1/30) + genesis_d_factor: 0.5 # start near true stake (cheap epoch 0) + early_stop: true diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py new file mode 100644 index 0000000..77b32c4 --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py @@ -0,0 +1,169 @@ +"""Comparison figures: countable uncle model (spec counting rules) vs the old model. + +Consumes the results of three sweeps: + + tsi-sweep --config configs/countable-vs-old.yaml --label cvo-countable + tsi-sweep --config configs/countable-vs-old.yaml --old --label cvo-old + tsi-sweep --config configs/absorption-window.yaml --label absorption-window + +and renders (into --out): + + cvo_accuracy_vs_delay equilibrium D/D_true vs Blend mixing delay; solid = countable, + dashed = old, one Okabe-Ito hue per U (color follows U). + cvo_prediction_vs_sim predicted log(1-f)/log(1-f/q_u) from the MEASURED q_u vs the + simulated equilibrium — the q -> q_u reduction check. + cvo_recovery_vs_delay measured recovery r = (q_eff - q)/(1 - q) and the first-fork + rejection share (deep_ref_share) vs delay. + absorption_window equilibrium vs the window absorption parameter W per delay. + +Usage: + python scripts/plot_countable_vs_old.py --countable RUNDIR --old RUNDIR \ + --absorption RUNDIR --out figures/countable-vs-old +""" + +from __future__ import annotations + +import argparse +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +from tsi_sim.plotting import style +from tsi_sim.plotting.figures_pernode import equilibrium +from tsi_sim.theory import expected_ratio + +DELAY = "blend_delay_max" + + +def _load(run_dir: str | Path) -> pd.DataFrame: + return pd.read_parquet(Path(run_dir) / "results.parquet") + + +def _eq(df: pd.DataFrame, extra_cols: tuple[str, ...] = ()) -> pd.DataFrame: + """Equilibrium (post-burn) means per (delay, U) cell, averaged over replicates.""" + eq = equilibrium(df) + keys = [DELAY, "max_uncles", *extra_cols] + agg = {"mean_ratio": "mean", "mean_q": "mean", "mean_q_eff": "mean"} + if "deep_ref_share" in eq.columns: + agg["deep_ref_share"] = "mean" + return eq.groupby(keys, as_index=False).agg(agg) + + +def fig_accuracy_vs_delay(cnt: pd.DataFrame, old: pd.DataFrame) -> plt.Figure: + fig, ax = plt.subplots() + us = sorted(cnt["max_uncles"].unique()) + for i, u in enumerate(us): + c = style.color_for(i) + a = cnt[cnt.max_uncles == u].sort_values(DELAY) + b = old[old.max_uncles == u].sort_values(DELAY) + ax.plot(a[DELAY], a.mean_ratio, "-o", color=c, label=f"U={u} countable", ms=4) + ax.plot(b[DELAY], b.mean_ratio, "--s", color=c, label=f"U={u} old", ms=4, + alpha=0.75) + ax.axhline(1.0, color="0.4", lw=0.8, ls=":") + ax.set_xlabel("max per-relay mixing delay (slots)") + ax.set_ylabel(r"equilibrium $\hat{D}/D_{true}$") + ax.set_title("Accuracy vs delay: countable (solid) vs old (dashed) uncle model") + ax.legend(ncol=2) + return fig + + +def fig_prediction_vs_sim(cnt: pd.DataFrame, f: float) -> plt.Figure: + fig, ax = plt.subplots(figsize=(4.6, 4.4)) + sub = cnt[cnt.max_uncles > 0] + pred = expected_ratio(f, sub.mean_q_eff.to_numpy()) + us = sorted(sub["max_uncles"].unique()) + for i, u in enumerate(us): + m = (sub.max_uncles == u).to_numpy() + ax.scatter(np.asarray(pred)[m], sub.mean_ratio.to_numpy()[m], + color=style.color_for(i), s=22, label=f"U={u}") + lo = min(float(np.min(pred)), float(sub.mean_ratio.min())) - 0.01 + ax.plot([lo, 1.005], [lo, 1.005], color="0.3", lw=0.9, ls=":", label="prediction = sim") + ax.set_xlabel(r"predicted $\log(1-f)\,/\,\log(1-f/\bar{q}_u)$ (measured $\bar{q}_u$)") + ax.set_ylabel(r"simulated equilibrium $\hat{D}/D_{true}$") + ax.set_title(r"$q \to q_u$ reduction: prediction vs simulation") + ax.legend() + return fig + + +def fig_recovery_vs_delay(cnt: pd.DataFrame) -> plt.Figure: + # Right panel: the non-recovered waste share 1-r (log scale). Under joint countable + # selection+counting the first-fork restriction acts at SELECTION (deep orphans are + # never referenced), so counting-side rejections (deep_ref_share) are 0 and the + # restriction shows up inside 1-r together with capacity losses. + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9.2, 3.8)) + us = [u for u in sorted(cnt["max_uncles"].unique()) if u > 0] + for i, u in enumerate(us): + a = cnt[cnt.max_uncles == u].sort_values(DELAY) + denom = np.maximum(1.0 - a.mean_q.to_numpy(), 1e-12) + r = (a.mean_q_eff.to_numpy() - a.mean_q.to_numpy()) / denom + ax1.plot(a[DELAY], r, "-o", color=style.color_for(i), label=f"U={u}", ms=4) + ax2.semilogy(a[DELAY], np.maximum(1.0 - r, 1e-4), "-o", + color=style.color_for(i), label=f"U={u}", ms=4) + ax1.set_xlabel("max per-relay mixing delay (slots)") + ax1.set_ylabel(r"measured recovery $r=(\bar{q}_u-\bar{q})/(1-\bar{q})$") + ax1.set_ylim(0, 1.02) + ax1.set_title("Uncle recovery rate") + ax1.legend() + ax2.set_xlabel("max per-relay mixing delay (slots)") + ax2.set_ylabel(r"non-recovered waste share $1-r$") + ax2.set_title("Residual (first-fork + capacity losses)") + ax2.legend() + return fig + + +def fig_absorption_window(absw: pd.DataFrame) -> plt.Figure: + fig, ax = plt.subplots() + eq = equilibrium(absw) + agg = eq.groupby([DELAY, "window_absorption"], as_index=False).mean_ratio.mean() + for i, d in enumerate(sorted(agg[DELAY].unique())): + a = agg[agg[DELAY] == d].sort_values("window_absorption") + ax.plot(a.window_absorption, a.mean_ratio, "-o", color=style.color_for(i), + label=f"delay={d:g}", ms=4) + ax.axhline(1.0, color="0.4", lw=0.8, ls=":") + ax.set_xlabel("window absorption parameter W (expected block-intervals)") + ax.set_ylabel(r"equilibrium $\hat{D}/D_{true}$") + ax.set_title("Accuracy vs the derived uncle window $w_u = W/f$ (U=1)") + ax.legend(title=None) + return fig + + +def main() -> None: + ap = argparse.ArgumentParser(description=__doc__.splitlines()[0]) + ap.add_argument("--countable", required=True, help="run dir of cvo-countable") + ap.add_argument("--old", required=True, help="run dir of cvo-old") + ap.add_argument("--absorption", required=True, help="run dir of absorption-window") + ap.add_argument("--out", default="figures/countable-vs-old") + args = ap.parse_args() + style.apply_style() + out = Path(args.out) + out.mkdir(parents=True, exist_ok=True) + + cnt_raw, old_raw = _load(args.countable), _load(args.old) + f = float(cnt_raw["f"].iloc[0]) + cnt, old = _eq(cnt_raw), _eq(old_raw) + prov = "tsi-sim-pernode countable-vs-old.yaml (+--old) / absorption-window.yaml" + + written = [] + written += style.save(fig_accuracy_vs_delay(cnt, old), out / "cvo_accuracy_vs_delay", prov) + written += style.save(fig_prediction_vs_sim(cnt, f), out / "cvo_prediction_vs_sim", prov) + written += style.save(fig_recovery_vs_delay(cnt), out / "cvo_recovery_vs_delay", prov) + written += style.save(fig_absorption_window(_load(args.absorption)), + out / "absorption_window", prov) + # headline numbers for the report / analysis doc + for u in sorted(cnt["max_uncles"].unique()): + for _, row in cnt[cnt.max_uncles == u].sort_values(DELAY).iterrows(): + q, qu = row.mean_q, row.mean_q_eff + r = (qu - q) / max(1.0 - q, 1e-12) + o = old[(old.max_uncles == u) & (old[DELAY] == row[DELAY])] + old_ratio = float(o.mean_ratio.iloc[0]) if len(o) else float("nan") + print(f"U={u} delay={row[DELAY]:>5g} countable={row.mean_ratio:.4f} " + f"old={old_ratio:.4f} q={q:.4f} q_u={qu:.4f} r={r:.4f} " + f"pred={float(expected_ratio(f, qu)):.4f} " + f"deep={row.get('deep_ref_share', float('nan')):.4f}") + print(f"wrote {len(written)} files -> {out}") + + +if __name__ == "__main__": + main() diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/blocktree.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/blocktree.py index 7d9b68b..f20d8d3 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/blocktree.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/blocktree.py @@ -364,7 +364,9 @@ def _build_pruned(active_slots, winners_per_slot, path_latency, config, rng, from .uncles import select_uncles_at_production NEG = np.iinfo(np.int64).min - keepspan = max(float(horizon), float(config.uncle_window)) # columns kept within this span + # columns kept within this span; the uncle window is model-dependent (derived W/f for + # countable, uncle_window slots for --old), so use the effective value. + keepspan = max(float(horizon), float(config.effective_uncle_window)) counts = np.array([int(g.shape[0]) for g in winners_per_slot], dtype=np.int64) cap = _max_span_blocks(active_slots, counts, keepspan) # max live blocks at once max_slot = int(counts.max()) if counts.size else 0 diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py index 76edec3..4f4951c 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py @@ -10,6 +10,16 @@ from . import constants StakeDist = Literal["uniform", "pareto"] UncleStrategy = Literal["oldest", "random"] +# Uncle counting/selection model: +# "countable" (default) — the spec's counting-only model (cryptarchia-v1-protocol.md): +# only the FIRST block of a fork is referenceable/countable (its parent lies on the +# referencing chain), the window is derived as w_u = window_absorption / f slots, +# selection excludes slots already occupied on the producer's chain and picks at most +# one uncle per slot, and counting re-checks every rule per reference. +# "old" — the pre-redesign model (run with --old): window = uncle_window slots directly, +# any orphan in view is referenceable regardless of fork depth, no occupied-slot or +# per-slot exclusion, and every baked reference counts. +UncleModel = Literal["countable", "old"] Topology = Literal["full_mesh", "regular", "blend"] LinkLatencyDist = Literal["fixed", "uniform", "exp", "geo"] JitterDist = Literal["exp", "poisson"] @@ -81,7 +91,14 @@ class SimConfig: jitter_frac: float = 1.0 # fraction of deliveries hit (poisson model; exp uses all) # --- uncle references --- - uncle_window: int = constants.W_DEFAULT # W + uncle_model: UncleModel = "countable" # countable (spec, default) | old (--old) + # Countable model: window absorption parameter W; the uncle reference window is DERIVED + # as w_u = W / f slots (W expected block-intervals), bounded 1 <= W <= 0.6*k + # (constants.W_ABS_MAX_FACTOR). Ignored by the old model. + window_absorption: float = constants.W_ABS_DEFAULT + # Old model only (--old): the uncle reference window w_u in slots, set directly. + # Ignored by the countable model, which derives the window from window_absorption. + uncle_window: int = constants.W_DEFAULT max_uncles: int = 0 # U (0 = baseline, no uncles) uncle_strategy: UncleStrategy = "oldest" # Coin-flip inclusion prob for the "random" strategy. Only 0.5 reproduces the spec's @@ -187,6 +204,25 @@ class SimConfig: raise ValueError(f"stake_dist must be uniform|pareto, got {self.stake_dist!r}") if self.uncle_strategy not in ("oldest", "random"): raise ValueError(f"uncle_strategy must be oldest|random, got {self.uncle_strategy!r}") + if self.uncle_model not in ("countable", "old"): + raise ValueError(f"uncle_model must be countable|old, got {self.uncle_model!r}") + if self.uncle_model == "countable": + if self.window_absorption < 1.0: + raise ValueError( + f"window_absorption W={self.window_absorption} must be >= 1") + if self.window_absorption > constants.W_ABS_MAX_FACTOR * self.k: + # The spec bounds W <= 0.6*k (w_u <= 0.6*k/f, inside the finalization + # window). Scaled-down research geometries (small k) may violate it on + # purpose — warn loudly rather than refuse, but full-scale runs should + # never see this. + import warnings + + warnings.warn( + f"window_absorption W={self.window_absorption} exceeds the spec bound " + f"{constants.W_ABS_MAX_FACTOR}*k = " + f"{constants.W_ABS_MAX_FACTOR * self.k:g} (k={self.k}); the derived " + f"window is outside the finalization window at this geometry", + RuntimeWarning, stacklevel=2) if self.topology not in ("full_mesh", "regular", "blend"): raise ValueError(f"topology must be full_mesh|regular|blend, got {self.topology!r}") if self.link_latency_dist not in ("fixed", "uniform", "exp", "geo"): @@ -264,6 +300,17 @@ class SimConfig: return (epoch % self.adversary_period) < self.adversary_withhold_epochs # derived geometry ------------------------------------------------------- + @property + def effective_uncle_window(self) -> int: + """The uncle reference window ``w_u`` in slots actually used by this run. + + Countable model (default): derived, ``w_u = round(window_absorption / f)``. + Old model (``--old``): ``uncle_window`` taken directly. + """ + if self.uncle_model == "old": + return self.uncle_window + return constants.uncle_window_slots(self.window_absorption, self.f) + @property def epoch_len(self) -> int: return constants.epoch_len(self.k, self.f) @@ -276,9 +323,12 @@ class SimConfig: """Hashable identity used to seed the RNG deterministically. Must include EVERY field that affects the run (guarded by test_rng), otherwise two - distinct configs would share an RNG stream. + distinct configs would share an RNG stream. ``uncle_model`` / + ``window_absorption`` are appended ONLY for the countable model: an ``--old`` run's + key is then byte-identical to the pre-redesign key, so ``--old`` bit-reproduces + historical runs (the two models still get distinct streams from the marker). """ - return ( + base = ( self.n_nodes, self.stake_dist, self.pareto_shape, self.uniform_random, self.total_stake, self.latency, self.latency_stochastic, self.uncle_window, self.max_uncles, self.uncle_strategy, self.uncle_random_p, self.f, self.beta, @@ -295,11 +345,15 @@ class SimConfig: # NOTE: windowed_fork_choice and prune_arrival are deliberately excluded — they are pure # compute/memory optimisations that consume no RNG and (at jitter_mean == 0) change no # result, so pruned and full-matrix runs must share a seed (see test_pernode parity). + if self.uncle_model == "old": + return base # historical (pre-uncle_model) key: --old bit-compat + return base + (self.uncle_model, self.window_absorption) # Axes that can be swept; every SimConfig field is legal here. _SWEEP_AXES = ( "n_nodes", "stake_dist", "latency", "max_uncles", "uncle_strategy", "uncle_window", + "window_absorption", "topology", "degree", "link_latency_mean", "link_latency_dist", "blend_hops", "blend_delay_max", "init_dest", "f", ) @@ -315,6 +369,7 @@ class SweepConfig: max_uncles: list[int] = field(default_factory=lambda: [0, 1, 2, 4]) uncle_strategy: list[UncleStrategy] = field(default_factory=lambda: ["oldest"]) uncle_window: list[int] = field(default_factory=lambda: [constants.W_DEFAULT]) + window_absorption: list[float] = field(default_factory=lambda: [constants.W_ABS_DEFAULT]) topology: list[Topology] = field(default_factory=lambda: ["regular"]) degree: list[int] = field(default_factory=lambda: [8]) link_latency_mean: list[float] = field(default_factory=lambda: [1.0]) @@ -333,11 +388,22 @@ class SweepConfig: axis_values = [getattr(self, ax) for ax in _SWEEP_AXES] for combo in itertools.product(*axis_values): overrides = dict(zip(_SWEEP_AXES, combo, strict=True)) - # U=0 references no uncles, so it is independent of uncle_strategy AND uncle_window; - # keep only the first of each to avoid duplicate (identical) work. + # U=0 references no uncles, so it is independent of uncle_strategy AND the window + # knobs; keep only the first of each to avoid duplicate (identical) work. if overrides["max_uncles"] == 0 and ( overrides["uncle_strategy"] != self.uncle_strategy[0] or overrides["uncle_window"] != self.uncle_window[0] + or overrides["window_absorption"] != self.window_absorption[0] + ): + continue + # each uncle model reads exactly one window knob — collapse the other axis so a + # sweep never emits duplicate cells that differ only in an ignored field. + if base.uncle_model == "countable" and ( + overrides["uncle_window"] != self.uncle_window[0] + ): + continue + if base.uncle_model == "old" and ( + overrides["window_absorption"] != self.window_absorption[0] ): continue # full mesh ignores degree / link-latency model; keep only the first to avoid dupes. diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/constants.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/constants.py index e4554d0..c69dda4 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/constants.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/constants.py @@ -10,10 +10,23 @@ from __future__ import annotations # --- True protocol values (full scale) ------------------------------------- K_TRUE = 2160 # security parameter (blocks) F = 1.0 / 30.0 # slot activation coefficient (default; configurable per run) -W_DEFAULT = 300 # uncle reference window w_u (slots) +W_DEFAULT = 300 # old model: uncle reference window w_u (slots), set directly (--old) BETA_DEFAULT = 1.0 # TSI learning rate SLOT_SECONDS = 1 # slot length (seconds) — so 1 slot == 1 s +# --- Countable uncle model (cryptarchia-v1-protocol.md, uncle references) --- +# The spec derives the uncle reference window from the *window absorption parameter* W: +# w_u = W * f^-1 slots, i.e. W expected block-intervals. W is bounded by 1 <= W <= 0.6*k, +# equivalently w_u <= 0.6*k/f = s/5, keeping the window strictly inside the finalization +# window. The default W = 10 reproduces w_u = 300 slots at f = 1/30. +W_ABS_DEFAULT = 10.0 # window absorption parameter W (expected block-intervals) +W_ABS_MAX_FACTOR = 0.6 # bound: W <= W_ABS_MAX_FACTOR * k + + +def uncle_window_slots(w_abs: float, f: float = F) -> int: + """Derived uncle reference window ``w_u = W / f`` in slots (countable model).""" + return max(1, int(round(w_abs / f))) + # --- Real-world inter-node network latency (per gossip link) --------------- # A slot is SLOT_SECONDS = 1 s, so measured internet latencies (tens–hundreds of ms) are diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/epoch.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/epoch.py index 7c1c820..d6e37bf 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/epoch.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/epoch.py @@ -30,6 +30,8 @@ class EpochResult: max_reorg_depth: int # deepest maximal orphan branch (blocks a reorg would discard) mean_reorg_depth: float # mean maximal-orphan-branch depth p_ref: float # emergent reference rate: in-window orphans referenced as uncles + deep_ref_share: float # share of examined references rejected by the parent-on-chain + # (first-fork) counting rule; 0 under the old model def _canonical_producer_split( @@ -101,7 +103,9 @@ def simulate_epoch( # measurement: each node's own canonical chain, deduped by tip + numba-accelerated ms = measure(tree, A, active_slots, T, cutoff=E, - legacy_block_count=config.legacy_block_count) + legacy_block_count=config.legacy_block_count, + countable=config.uncle_model != "old", + w=config.effective_uncle_window) n_active_window = int((active_slots < T).sum()) d_next = tsi.update_D_vec(d_est, ms.m, T, f, config.beta, config.fixed_point) @@ -109,6 +113,8 @@ def simulate_epoch( attribution = coalition_mask if coalition_mask is not None else adversary_mask adv_blocks, honest_blocks = _canonical_producer_split(tree, A, attribution, T, E) fork_rate, max_reorg_depth, mean_reorg_depth, p_ref = fork.fork_stats(tree, A, T, cutoff=E) + ref_total = int(ms.ref_total.sum()) + deep_ref_share = (int(ms.ref_deep.sum()) / ref_total) if ref_total else 0.0 return EpochResult( d_next=d_next, m=ms.m, q=ms.q, q_eff=ms.q_eff, n_blocks=tree.n_blocks - 1, @@ -117,5 +123,5 @@ def simulate_epoch( mean_orphan_rate=float(ms.orphan_rate.mean()), adv_blocks=adv_blocks, honest_blocks=honest_blocks, fork_rate=fork_rate, max_reorg_depth=max_reorg_depth, mean_reorg_depth=mean_reorg_depth, - p_ref=p_ref, + p_ref=p_ref, deep_ref_share=deep_ref_share, ) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py index 9db0c57..80945c2 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py @@ -6,6 +6,16 @@ independently — O(N x chain) Python and ~95% of an epoch. Two exact optimisati The counted density ``m`` is SLOT-based (canonical slots + recovered uncle slots — the "one count per slot" invariant; ``legacy_block_count`` reproduces the old per-block count). +Counting models (``countable`` flag; CLI ``--old`` clears it): + +* **countable** (default) — the spec's counting rules are re-checked per reference + (cryptarchia-v1-protocol.md): the reference must be within the window + (``0 < slot_B - slot_U <= w``), the uncle must not lie on the counting chain, and its + **parent must lie on the counting chain** (only the first block of a fork counts). + References failing the parent rule are tallied as ``deep`` diagnostics. +* **old** — every baked reference in the measurement window counts (fork depth ignored), + reproducing the pre-redesign behaviour. + 1. **Dedup by tip.** Nodes sharing a current tip share their whole canonical chain and every derived quantity, so we compute once per *distinct* tip and broadcast. High node agreement (the common case) collapses N to a handful of computations. @@ -41,6 +51,9 @@ class Measurement: q: np.ndarray # (N,) honest active-slot fraction q_eff: np.ndarray # (N,) uncle-recovered fraction orphan_rate: np.ndarray # (N,) + ref_total: np.ndarray # (N,) distinct referenced uncles examined in the window + ref_deep: np.ndarray # (N,) of those, rejected by the parent-on-chain (first-fork) rule; + # always 0 under the old model (no rule to reject on) agreement_window: float agreement_tip: float @@ -58,23 +71,26 @@ def _uncles_csr(tree: BlockTree) -> tuple[np.ndarray, np.ndarray]: return flat, ptr -def _measure_tips_py(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, - uncle_stamp, honest_stamp): +def _measure_tips_py(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, w, countable, + uncle_stamp, honest_stamp, chain_stamp): """Pure-Python per-distinct-tip walk (fallback / reference for the kernel).""" K = distinct_tips.shape[0] m = np.empty(K, np.int64) n_honest = np.empty(K, np.int64) n_rec = np.empty(K, np.int64) + n_ref = np.empty(K, np.int64) + n_deep = np.empty(K, np.int64) chain_len = np.empty(K, np.int64) fp = np.empty(K, np.uint64) for ki in range(K): - # pass 1: chain -> honest count, mark honest slots, fingerprint, chain length + # pass 1: chain -> honest count, mark honest slots + chain membership, fingerprint honest = 0 clen = 0 f = np.uint64(0) b = int(distinct_tips[ki]) while b > 0: clen += 1 + chain_stamp[b] = ki # chain membership (any slot, incl. outside T) s = int(slot[b]) if 0 <= s < T: honest += 1 @@ -84,13 +100,27 @@ def _measure_tips_py(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, # pass 2: deduped referenced uncles in window + recovered orphan slots ucnt = 0 rec = 0 + refs = 0 + deep = 0 b = int(distinct_tips[ki]) while b > 0: for j in range(int(uncle_ptr[b]), int(uncle_ptr[b + 1])): u = int(uncle_flat[j]) su = int(slot[u]) if 0 <= su < T and uncle_stamp[u] != ki: - uncle_stamp[u] = ki # dedup uncles by id (m counts blocks) + uncle_stamp[u] = ki # dedup uncles by id + refs += 1 + if countable: + # spec counting rules, re-checked per reference: + d = int(slot[b]) - su + if d <= 0 or d > w: + continue # outside the reference window + if chain_stamp[u] == ki: + continue # uncle lies on the counting chain + pu = int(parent[u]) + if pu != 0 and chain_stamp[pu] != ki: + deep += 1 # not a first fork block: uncounted + continue ucnt += 1 if honest_stamp[su] != ki: rec += 1 # recovered slots deduped by slot @@ -99,9 +129,11 @@ def _measure_tips_py(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, m[ki] = honest + ucnt n_honest[ki] = honest n_rec[ki] = rec + n_ref[ki] = refs + n_deep[ki] = deep chain_len[ki] = clen fp[ki] = f - return m, n_honest, n_rec, chain_len, fp + return m, n_honest, n_rec, n_ref, n_deep, chain_len, fp def _mix_py(x: np.uint64) -> np.uint64: @@ -119,12 +151,14 @@ if _HAVE_NUMBA: return x ^ (x >> uint64(31)) @njit(cache=True) - def _measure_tips_nb(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, - uncle_stamp, honest_stamp): + def _measure_tips_nb(distinct_tips, parent, slot, uncle_flat, uncle_ptr, T, w, countable, + uncle_stamp, honest_stamp, chain_stamp): K = distinct_tips.shape[0] m = np.empty(K, np.int64) n_honest = np.empty(K, np.int64) n_rec = np.empty(K, np.int64) + n_ref = np.empty(K, np.int64) + n_deep = np.empty(K, np.int64) chain_len = np.empty(K, np.int64) fp = np.empty(K, np.uint64) for ki in range(K): @@ -134,6 +168,7 @@ if _HAVE_NUMBA: b = distinct_tips[ki] while b > 0: clen += 1 + chain_stamp[b] = ki # chain membership (any slot, incl. outside T) s = slot[b] if 0 <= s < T: honest += 1 @@ -142,6 +177,8 @@ if _HAVE_NUMBA: b = parent[b] ucnt = 0 rec = 0 + refs = 0 + deep = 0 b = distinct_tips[ki] while b > 0: for j in range(uncle_ptr[b], uncle_ptr[b + 1]): @@ -149,25 +186,45 @@ if _HAVE_NUMBA: su = slot[u] if 0 <= su < T and uncle_stamp[u] != ki: uncle_stamp[u] = ki # dedup uncles by id - ucnt += 1 - if honest_stamp[su] != ki: - rec += 1 # recovered slots deduped by slot - honest_stamp[su] = ki + refs += 1 + ok = True + if countable: + d = slot[b] - su + if d <= 0 or d > w: + ok = False # outside the reference window + elif chain_stamp[u] == ki: + ok = False # uncle lies on the counting chain + else: + pu = parent[u] + if pu != 0 and chain_stamp[pu] != ki: + deep += 1 # not a first fork block: uncounted + ok = False + if ok: + ucnt += 1 + if honest_stamp[su] != ki: + rec += 1 # recovered slots deduped by slot + honest_stamp[su] = ki b = parent[b] m[ki] = honest + ucnt n_honest[ki] = honest n_rec[ki] = rec + n_ref[ki] = refs + n_deep[ki] = deep chain_len[ki] = clen fp[ki] = f - return m, n_honest, n_rec, chain_len, fp + return m, n_honest, n_rec, n_ref, n_deep, chain_len, fp def measure(tree: BlockTree, A, active_slots: np.ndarray, T: int, cutoff: int, - use_numba: bool = True, legacy_block_count: bool = False) -> Measurement: + use_numba: bool = True, legacy_block_count: bool = False, + countable: bool = False, w: int = 0) -> Measurement: """Per-node m/q/q_eff + agreement, deduped by tip and (optionally) numba-accelerated. - ``A`` is the full ``(N, n_blocks)`` arrival matrix or a pruned ``SlidingArrival`` — only - ``tips_for_all_nodes`` reads it, so ``N`` is taken from the returned per-node tips. + ``countable`` applies the spec's per-reference counting rules (window ``w``, + not-on-chain, parent-on-chain); ``countable=False`` reproduces the old model where every + baked reference counts. ``A`` is the full ``(N, n_blocks)`` arrival matrix or a pruned + ``SlidingArrival`` — only ``tips_for_all_nodes`` reads it, so ``N`` is taken from the + returned per-node tips. """ tips = tips_for_all_nodes(tree, A, cutoff) N = tips.shape[0] @@ -179,11 +236,13 @@ def measure(tree: BlockTree, A, active_slots: np.ndarray, T: int, cutoff: int, uncle_flat, uncle_ptr = _uncles_csr(tree) uncle_stamp = np.full(tree.n_blocks, -1, np.int64) honest_stamp = np.full(max(T, 1), -1, np.int64) + chain_stamp = np.full(tree.n_blocks, -1, np.int64) kernel = _measure_tips_nb if (_HAVE_NUMBA and use_numba) else _measure_tips_py - m_d, nh_d, nrec_d, clen_d, fp_d = kernel( + m_d, nh_d, nrec_d, nref_d, ndeep_d, clen_d, fp_d = kernel( distinct_tips.astype(np.int64), tree.parent, tree.slot, - uncle_flat, uncle_ptr, np.int64(T), uncle_stamp, honest_stamp) + uncle_flat, uncle_ptr, np.int64(T), np.int64(w), bool(countable), + uncle_stamp, honest_stamp, chain_stamp) # correct slot counting: canonical slots + recovered (non-canonical, deduped) uncle slots. # legacy_block_count reproduces the earlier per-block-id count (kernel's m = honest + ucnt). @@ -200,4 +259,5 @@ def measure(tree: BlockTree, A, active_slots: np.ndarray, T: int, cutoff: int, agreement_window = max(fp_counts.values()) / N return Measurement(m=m, q=q, q_eff=q_eff, orphan_rate=orphan_rate, + ref_total=nref_d[inverse], ref_deep=ndeep_d[inverse], agreement_window=agreement_window, agreement_tip=agreement_tip) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py index 6d933ab..79587f2 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py @@ -13,7 +13,8 @@ from .epoch import EpochResult _CONFIG_FIELDS = ( "n_nodes", "stake_dist", "pareto_shape", "latency", "topology", "degree", "link_latency_mean", "link_latency_dist", "blend_hops", "blend_delay_max", - "init_dest", "init_spread", "uncle_window", "max_uncles", "uncle_strategy", + "init_dest", "init_spread", "uncle_model", "window_absorption", + "uncle_window", "max_uncles", "uncle_strategy", "f", "beta", "k", "genesis_d_factor", "epochs", "fixed_point", "legacy_block_count", "replicate", "adversary_frac", "adversary_strategy", "adversary_period", "adversary_withhold_epochs", @@ -58,5 +59,6 @@ def divergence_row( max_reorg_depth=er.max_reorg_depth, mean_reorg_depth=er.mean_reorg_depth, p_ref=er.p_ref, + deep_ref_share=er.deep_ref_share, ) return row diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py index 9f08222..e7c3164 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py @@ -18,8 +18,8 @@ from . import style # this exhaustive over the recorded config fields (see metrics._CONFIG_FIELDS). CONFIG_COLS = ["n_nodes", "stake_dist", "pareto_shape", "topology", "degree", "link_latency_mean", "link_latency_dist", "blend_hops", "blend_delay_max", - "latency", "max_uncles", "uncle_strategy", "uncle_window", - "init_dest", "init_spread", "genesis_d_factor", + "latency", "uncle_model", "window_absorption", "max_uncles", "uncle_strategy", + "uncle_window", "init_dest", "init_spread", "genesis_d_factor", "f", "beta", "k", "fixed_point", "legacy_block_count"] # Graph topologies (as opposed to the full_mesh baseline) and the dominant latency knob each @@ -41,12 +41,15 @@ def equilibrium(df: pd.DataFrame, burn_frac: float = 0.5) -> pd.DataFrame: ``epochs`` — early-stopped runs (config.early_stop) terminate well before the planned ``epochs``, so thresholding on the configured value would drop every row. """ - max_epoch = df.groupby([*CONFIG_COLS, "replicate"])["epoch"].transform("max") + cfg_cols = [c for c in CONFIG_COLS if c in df.columns] # old parquets lack new fields + max_epoch = df.groupby([*cfg_cols, "replicate"])["epoch"].transform("max") tail = df[df["epoch"] >= max_epoch * burn_frac] agg = {c: (c, "mean") for c in ("mean_ratio", "range_ratio", "iqr_ratio", "agreement_window", "agreement_tip", - "mean_q", "mean_q_eff", "mean_orphan_rate", "max_ratio", "min_ratio")} - return tail.groupby([*CONFIG_COLS, "replicate"], as_index=False).agg(**agg) + "mean_q", "mean_q_eff", "mean_orphan_rate", "max_ratio", "min_ratio", + "deep_ref_share", "p_ref", "fork_rate") + if c in tail.columns} + return tail.groupby([*cfg_cols, "replicate"], as_index=False).agg(**agg) def _prov(df: pd.DataFrame) -> str: diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/sweep.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/sweep.py index ecc3d4a..2f53bd1 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/sweep.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/sweep.py @@ -77,7 +77,7 @@ def _arrival_columns(config: SimConfig, peak_blocks: int) -> int: if not (config.prune_arrival and config.windowed_fork_choice): return peak_blocks per_slot = peak_blocks / config.epoch_len if config.epoch_len else peak_blocks - keepspan = float(config.uncle_window) + keepspan = float(config.effective_uncle_window) if config.topology == "blend": lat = max(config.link_latency_mean, 0.1) keepspan = max(keepspan, (config.blend_hops + 1) * lat * 4 @@ -314,19 +314,26 @@ def main(argv: list[str] | None = None) -> None: "(default) probes when N>2000, 'always', or 'never' (estimate only)") parser.add_argument("--no-figures", action="store_true", help="skip auto figure generation") + parser.add_argument("--old", action="store_true", + help="run the old (pre countable redesign) uncle model: window = " + "uncle_window slots, any-depth orphans referenceable, every " + "baked reference counts; bit-reproduces historical runs") args = parser.parse_args(argv) batch_size = int(args.batch_size) if args.batch_size != "auto" else "auto" - label = args.label or Path(args.config).stem + label = args.label or (Path(args.config).stem + ("-old" if args.old else "")) run_dir = new_run_dir(args.outdir, label) sweep = load_sweep_yaml(args.config) + if args.old: + sweep.base["uncle_model"] = "old" df = run_sweep(sweep, n_jobs=args.n_jobs, batch_size=batch_size, mem_frac=args.mem_frac, calibrate=args.calibrate) results_path = run_dir / "results.parquet" persist(df, results_path) key_cols = ["n_nodes", "stake_dist", "topology", "degree", "link_latency_mean", - "latency", "max_uncles", "uncle_strategy", "init_dest", "replicate"] + "latency", "uncle_model", "max_uncles", "uncle_strategy", "init_dest", + "replicate"] n_cfg = len(df[key_cols].drop_duplicates()) print(f"wrote {len(df)} rows ({n_cfg} configs) -> {results_path}") diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py index cb96976..42283a0 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/theory.py @@ -18,6 +18,30 @@ def expected_ratio(f: float, q: ArrayLike) -> ArrayLike: return np.log(1.0 - f) / np.log(1.0 - f / q) +def q_effective(q: ArrayLike, r: ArrayLike) -> ArrayLike: + """Effective slot utilisation with uncle recovery: ``q_u = q + (1 - q) r``. + + ``r`` is the recovery rate — the probability that a wasted active slot is recovered by a + countable referenced uncle. Recovery is a binomial thinning of the waste + (``n ~ Bin(p, A)`` wasted, ``u | n ~ Bin(r, n)`` recovered, so the residual waste is + ``Bin(p(1-r), A)``), hence every closed-form result above holds verbatim with ``q`` + replaced by ``q_u``. Full recovery (``r = 1``) gives ``q_u = 1`` and an unbiased + equilibrium; ``r = 0`` reduces to the chain-only ``q``. + """ + q = np.asarray(q, dtype=float) + r = np.asarray(r, dtype=float) + return q + (1.0 - q) * r + + +def window_miss_prob(f: float, w_abs: ArrayLike) -> ArrayLike: + """P(no canonical block appears within the uncle window ``w_u = W/f``) — the window's + contribution to non-recovery: ``(1-f)^(W/f) ~ e^-W`` (4.5e-5 at the default W = 10). + The absorption parameter W therefore controls the miss probability directly. + """ + w_abs = np.asarray(w_abs, dtype=float) + return (1.0 - f) ** (w_abs / f) + + def block_count_ceiling(f: float) -> float: """LEGACY-mode ceiling: the equilibrium ratio under ``legacy_block_count=True``. diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/tsi.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/tsi.py index 29d5f25..32d1f45 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/tsi.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/tsi.py @@ -19,30 +19,61 @@ from .blocktree import BlockTree def referenced_uncle_ids(tree: BlockTree, canonical_ids: list[int]) -> set[int]: - """Deduplicated set of uncle ids referenced by the canonical chain.""" + """Deduplicated set of uncle ids referenced by the canonical chain (old model: all).""" ref: set[int] = set() for b in canonical_ids: ref.update(tree.uncles[b]) return ref +def countable_refs(tree: BlockTree, canonical_ids: list[int], w: int) -> set[int]: + """Deduplicated set of COUNTABLE referenced uncles (spec counting rules). + + A reference ``u`` of canonical block ``b`` is countable iff ``u`` is not itself + canonical, ``0 < slot_b - slot_u <= w``, and ``u``'s parent lies on the canonical chain + (only the first block of a fork counts) — the per-reference re-check of + cryptarchia-v1-protocol.md's counting rules. Reference implementation for the + measurement kernel (see test_measure / test_tsi_counting). + """ + canon = set(canonical_ids) + out: set[int] = set() + for b in canonical_ids: + sb = int(tree.slot[b]) + for u in tree.uncles[b]: + if u in canon: + continue # uncle lies on the counting chain + du = sb - int(tree.slot[u]) + if not 0 < du <= w: + continue # outside the reference window + p = int(tree.parent[u]) + if p != 0 and p not in canon: + continue # not a first fork block (deep): uncounted + out.add(u) + return out + + def _in_window(slot: int, T: int) -> bool: return 0 <= slot < T def density_m(tree: BlockTree, canonical_ids: list[int], T: int, - legacy_block_count: bool = False) -> int: + legacy_block_count: bool = False, + countable: bool = False, w: int = 0) -> int: """Slot count ``m`` for the TSI update: canonical slots + recovered uncle slots. A slot counts at most once: canonical blocks occupy distinct slots by construction, and a referenced uncle contributes only if its slot is not already canonical-occupied (and - only once per slot, however many same-slot uncles are referenced). ``legacy_block_count`` - reproduces the earlier per-block-id counting (double-counts multi-winner slots). + only once per slot, however many same-slot uncles are referenced). ``countable`` applies + the spec's per-reference counting rules via :func:`countable_refs` (window ``w``); + ``countable=False`` is the old model where every baked reference counts. + ``legacy_block_count`` reproduces the earlier per-block-id counting (double-counts + multi-winner slots). """ s = tree.slot[canonical_ids] in_win = (s >= 0) & (s < T) honest = int(in_win.sum()) - ref = referenced_uncle_ids(tree, canonical_ids) + ref = (countable_refs(tree, canonical_ids, w) if countable + else referenced_uncle_ids(tree, canonical_ids)) if legacy_block_count: return honest + sum(1 for u in ref if _in_window(int(tree.slot[u]), T)) canon_slots = set(int(x) for x in s[in_win]) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py index dfe8b42..04cc065 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py @@ -1,13 +1,21 @@ """Proposer-local uncle selection. -For each canonical block ``B`` (processed oldest-first so ancestors' references are -known), candidates are orphan (non-canonical) blocks ``U`` with -``0 < slot_B - slot_U <= W`` that have not already been referenced by an ancestor of -``B``. Two strategies match the spec: deterministic oldest-first, and random (oldest-first -order, a coin of probability ``uncle_random_p`` per candidate, capped at ``U``). The spec's -coin is unbiased (``uncle_random_p = 0.5``, the default); other values are a non-spec -sensitivity knob. Dedup across ancestors is enforced by threading a ``referenced`` set down -the canonical chain. +Two models, switched by ``config.uncle_model`` (CLI: ``--old``): + +**countable** (default) — the spec's counting-only model (cryptarchia-v1-protocol.md, +Uncle Selection): candidates are orphan blocks in the producer's view within the DERIVED +window ``w_u = window_absorption / f`` whose **parent lies on the producer's chain** (only +the first block of a fork is countable), excluding candidates whose slot is already +occupied on that chain (by a canonical block or an already-referenced uncle), and picking +at most one uncle per slot, oldest-first (or the ``random`` sensitivity knob). + +**old** (pre-redesign; kept verbatim for ``--old`` reproduction) — candidates are ANY +orphan blocks in view with ``0 < slot_B - slot_U <= uncle_window``, regardless of fork +depth, that are not on the producer's chain and not already referenced by it; dedup is by +block id only (no slot exclusion). + +Selected refs are baked at production and immutable once adopted, so density counting +stays view-independent under both models. """ from __future__ import annotations @@ -32,39 +40,77 @@ def _orphans_sorted(tree: BlockTree, canonical_ids: list[int]) -> tuple[np.ndarr def annotate_uncles( tree: BlockTree, canonical_ids: list[int], config: SimConfig, rng: np.random.Generator ) -> None: - """Fill ``tree.uncles[B]`` for every canonical block ``B`` per the selection rule.""" + """Fill ``tree.uncles[B]`` for every canonical block ``B`` per the selection rule (offline). + + Countable model: candidates are restricted to orphans whose parent is canonical (first + fork blocks), slots already occupied on the chain are excluded, and at most one uncle + per slot is picked. Old model: any orphan in the window, dedup by id only. + """ u_max = config.max_uncles if u_max <= 0: return - w = config.uncle_window + w = config.effective_uncle_window orphan_ids, orphan_slots = _orphans_sorted(tree, canonical_ids) if orphan_ids.size == 0: return + countable = config.uncle_model != "old" + occupied: set[int] = set() + if countable: + canonical = set(canonical_ids) + keep = [i for i in range(orphan_ids.size) + if int(tree.parent[orphan_ids[i]]) == GENESIS + or int(tree.parent[orphan_ids[i]]) in canonical] + orphan_ids, orphan_slots = orphan_ids[keep], orphan_slots[keep] + if orphan_ids.size == 0: + return + occupied = {int(tree.slot[b]) for b in canonical_ids} + referenced: set[int] = set() # oldest canonical block first for b in reversed(canonical_ids): sb = int(tree.slot[b]) - lo = int(np.searchsorted(orphan_slots, sb - w, side="left")) # slot_U >= sb - W + lo = int(np.searchsorted(orphan_slots, sb - w, side="left")) # slot_U >= sb - w hi = int(np.searchsorted(orphan_slots, sb, side="left")) # slot_U < sb if hi <= lo: continue window_ids = orphan_ids[lo:hi] # already oldest-first - selected = _select(window_ids, referenced, config, rng) + if countable: + window_ids = np.array( + [x for x in window_ids.tolist() if int(tree.slot[x]) not in occupied], + dtype=np.int64, + ) + selected = _select(window_ids, referenced, config, rng, + slot=tree.slot, one_per_slot=countable) if selected: tree.uncles[b] = tuple(selected) referenced.update(selected) + if countable: + occupied.update(int(tree.slot[u]) for u in selected) def _select( - window_ids: np.ndarray, referenced: set[int], config: SimConfig, rng: np.random.Generator + window_ids: np.ndarray, + referenced: set[int], + config: SimConfig, + rng: np.random.Generator, + slot: np.ndarray | None = None, + one_per_slot: bool = False, ) -> list[int]: + """Pick up to ``max_uncles`` candidates. ``one_per_slot`` adds the countable model's + per-slot dedup (a second same-slot candidate adds no occupied slot, so it is skipped).""" u_max = config.max_uncles out: list[int] = [] + slots_taken: set[int] = set() if config.uncle_strategy == "oldest": for bid in window_ids.tolist(): if bid in referenced: continue + if one_per_slot: + s = int(slot[bid]) + if s in slots_taken: + continue + slots_taken.add(s) out.append(bid) if len(out) >= u_max: break @@ -73,7 +119,11 @@ def _select( for bid in window_ids.tolist(): if bid in referenced: continue + if one_per_slot and int(slot[bid]) in slots_taken: + continue if rng.random() < p: + if one_per_slot: + slots_taken.add(int(slot[bid])) out.append(bid) if len(out) >= u_max: break @@ -96,21 +146,24 @@ def select_uncles_at_production( ) -> tuple[int, ...]: """Uncles a block gets when produced by node ``v`` (arrival row ``arrival_v``) at slot ``t``. - Candidates are blocks in ``v``'s view (``arrival_v[b] <= t``) with slot in ``[t-W, t)`` - that are NOT on the chain ``v`` extends (ancestors of ``parent_id``) and not already - referenced by that chain. Selected once and baked globally (same for everyone who adopts - the block), so density counting stays view-independent. + Candidates are blocks in ``v``'s view (``arrival_v[b] <= t``) with slot in + ``[t-w_u, t)`` that are NOT on the chain ``v`` extends (ancestors of ``parent_id``) and + not already referenced by that chain; the countable model (default) additionally + requires the candidate's **parent to lie on that chain** (first block of its fork), + excludes candidates whose slot is already occupied on the chain, and picks at most one + per slot. Selected once and baked globally (same for everyone who adopts the block), so + density counting stays view-independent. ``arrival_v`` is indexed by *block id minus ``arr_base``* — ``arr_base=0`` for the full arrival matrix row ``A[v]``, or the sliding-window buffer's base offset when pruning (every uncle-window - block ``[t-W, t)`` is inside the kept span, so the buffer row covers all candidates). + block ``[t-w_u, t)`` is inside the kept span, so the buffer row covers all candidates). """ u_max = config.max_uncles if u_max <= 0: return () - w = config.uncle_window + w = config.effective_uncle_window slot_view = slot[:nb] - lo = int(np.searchsorted(slot_view, t - w, side="left")) # slot >= t-W + lo = int(np.searchsorted(slot_view, t - w, side="left")) # slot >= t-w_u hi = int(np.searchsorted(slot_view, t, side="left")) # slot < t if hi <= lo: return () @@ -118,18 +171,61 @@ def select_uncles_at_production( arrived = np.nonzero(arrival_v[lo - arr_base:hi - arr_base] <= t)[0] + lo if arrived.size == 0: return () - # v's own chain within the window + the uncles it already references (for dedup) - on_chain: set[int] = set() - referenced: set[int] = set() + + if config.uncle_model == "old": + # --- old model (pre countable redesign; kept verbatim for --old) ---------------- + # v's own chain within the window + the uncles it already references (for dedup) + on_chain: set[int] = set() + referenced: set[int] = set() + a = int(parent_id) + while a > GENESIS and int(slot[a]) >= t - w: + on_chain.add(a) + referenced.update(uncles[a]) + a = int(parent[a]) + cands = np.array( + [b for b in arrived.tolist() + if b > GENESIS and b not in on_chain and b not in referenced], + dtype=np.int64, + ) + if cands.size == 0: + return () + return tuple(_select(cands, set(), config, rng)) # cands already oldest-first (slot,id) + + # --- countable model (spec counting rules; the default) ----------------------------- + # Window walk over v's chain: chain blocks, their referenced uncles, and the slots both + # occupy (the spec's occupied-slot exclusion in Uncle Selection). + on_chain = set() + referenced = set() + occupied: set[int] = set() a = int(parent_id) while a > GENESIS and int(slot[a]) >= t - w: on_chain.add(a) - referenced.update(uncles[a]) + occupied.add(int(slot[a])) + for u in uncles[a]: + referenced.add(u) + su = int(slot[u]) + if su >= t - w: + occupied.add(su) a = int(parent[a]) + pre = [b for b in arrived.tolist() + if b > GENESIS and b not in on_chain and b not in referenced + and int(slot[b]) not in occupied] + if not pre: + return () + # Parent-on-chain (only the first block of a fork is countable): the window walk covers + # parents inside the window; extend chain membership exactly far enough below it to + # decide the oldest candidate parent (cheap — parents are typically recent). + pmin = min(int(slot[int(parent[b])]) for b in pre) + below: set[int] = set() + while a > GENESIS and int(slot[a]) >= pmin: + below.add(a) + a = int(parent[a]) + chain_ids = on_chain | below cands = np.array( - [b for b in arrived.tolist() if b > GENESIS and b not in on_chain and b not in referenced], + [b for b in pre if int(parent[b]) == GENESIS or int(parent[b]) in chain_ids], dtype=np.int64, ) if cands.size == 0: return () - return tuple(_select(cands, set(), config, rng)) # cands already oldest-first (slot,id) + # cands already oldest-first (slot, id); one uncle per slot per the spec's selection. + return tuple(_select(cands, set(), config, rng, slot=slot, one_per_slot=True)) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/verify.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/verify.py index 411a6a6..1f91e3b 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/verify.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/verify.py @@ -38,9 +38,18 @@ def check(name: str, ok: bool, detail: str) -> bool: return ok -def main() -> int: +def main(argv: list[str] | None = None) -> int: + import argparse + + ap = argparse.ArgumentParser(description="Per-node TSI analytic checks") + ap.add_argument("--old", action="store_true", + help="run the old (pre countable redesign) uncle model") + args = ap.parse_args(argv) + uncle_model = "old" if args.old else "countable" + results = [] - common = dict(n_nodes=300, stake_dist="uniform", k=K, epochs=EPOCHS, genesis_d_factor=0.5) + common = dict(n_nodes=300, stake_dist="uniform", k=K, epochs=EPOCHS, genesis_d_factor=0.5, + uncle_model=uncle_model) # 1. Full-mesh baseline: zero per-node divergence, full window agreement. fm = SimConfig(topology="full_mesh", latency=4, max_uncles=0, **common) diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py index a40f395..26e47fa 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py @@ -85,13 +85,15 @@ def test_blend_dedup_does_not_multiply_non_blend_configs(): def test_uncle_window_sweeps_and_collapses_for_u0(): - # uncle_window is a live axis for U>0, but U=0 references no uncles so it must collapse. + # OLD model: uncle_window is a live axis for U>0, but U=0 references no uncles so it + # must collapse. (The countable model ignores uncle_window entirely — see the twin + # test below.) sweep = SweepConfig( n_nodes=[100], stake_dist=["uniform"], topology=["blend"], degree=[6], link_latency_mean=[0.5], link_latency_dist=["geo"], blend_hops=[3], blend_delay_max=[4.0], uncle_window=[10, 100], max_uncles=[0, 1], uncle_strategy=["oldest"], init_dest=["common"], replicates=1, - base={"k": 8, "epochs": 3}, + base={"k": 8, "epochs": 3, "uncle_model": "old"}, ) configs = sweep.expand() u0 = [c for c in configs if c.max_uncles == 0] @@ -100,6 +102,24 @@ def test_uncle_window_sweeps_and_collapses_for_u0(): assert {c.uncle_window for c in u1} == {10, 100} # both W kept for U=1 +def test_window_absorption_sweeps_and_ignored_axis_collapses(): + # COUNTABLE model: window_absorption is the live window axis; uncle_window is ignored + # and must collapse. And vice versa for the old model (guarded above). + sweep = SweepConfig( + n_nodes=[100], stake_dist=["uniform"], topology=["blend"], degree=[6], + link_latency_mean=[0.5], link_latency_dist=["geo"], blend_hops=[3], + blend_delay_max=[4.0], uncle_window=[10, 100], window_absorption=[2.0, 4.0], + max_uncles=[0, 1], uncle_strategy=["oldest"], init_dest=["common"], replicates=1, + base={"k": 8, "epochs": 3}, + ) + configs = sweep.expand() + u0 = [c for c in configs if c.max_uncles == 0] + u1 = [c for c in configs if c.max_uncles == 1] + assert len(u0) == 1 # all window knobs collapse + assert {c.window_absorption for c in u1} == {2.0, 4.0} # live axis kept for U=1 + assert {c.uncle_window for c in u1} == {10} # ignored axis collapsed + + def test_unknown_sweep_key_rejected(): with pytest.raises(ValueError, match="unknown sweep keys"): SweepConfig.from_dict({"latencies": [0, 1], "base": {}}) # typo: latencies vs latency @@ -117,7 +137,11 @@ def test_key_covers_every_field(): # optimisation (no RNG, identical results) so it is intentionally not in key(). # early_stop is truncation-only (per-epoch RNG streams are pre-spawned, so the epochs # that DO run are bit-identical to a full run's prefix) — intentionally excluded from key(). - ignored = {"root_seed", "windowed_fork_choice", "prune_arrival", "early_stop"} + # uncle_window is read ONLY by the old model; under the (default) countable model it is + # an ignored field, deliberately left in the base tuple at its old position so that an + # --old run's key stays byte-identical to historical keys. + ignored = {"root_seed", "windowed_fork_choice", "prune_arrival", "early_stop", + "uncle_window"} names = {f.name for f in dataclasses.fields(SimConfig)} - ignored a = SimConfig() for name in names: @@ -125,6 +149,42 @@ def test_key_covers_every_field(): alt = _perturb(cur) b = dataclasses.replace(a, **{name: alt}) assert a.key() != b.key(), f"key() does not distinguish field {name!r}" + # ... and uncle_window IS distinguished under the old model, where it is live. + old = SimConfig(uncle_model="old") + assert old.key() != dataclasses.replace(old, uncle_window=old.uncle_window + 1).key() + + +def test_old_model_key_is_historical(): + # --old must bit-reproduce historical runs: its key is exactly the pre-uncle_model + # tuple (no uncle_model / window_absorption entries), and the countable key extends it. + old = SimConfig(uncle_model="old") + new = SimConfig() + assert new.key()[: len(old.key())] == old.key() + assert new.key()[len(old.key()):] == ("countable", new.window_absorption) + # window_absorption is ignored (and absent from key) under the old model... + assert dataclasses.replace(old, window_absorption=2.0).key() == old.key() + # ...and live under the countable model. + assert dataclasses.replace(new, window_absorption=2.0).key() != new.key() + + +def test_effective_uncle_window(): + # countable: derived w_u = round(W / f); old: uncle_window taken directly. + assert SimConfig(k=2160).effective_uncle_window == 300 # W=10, f=1/30 + assert SimConfig(k=2160, window_absorption=5.0).effective_uncle_window == 150 + assert SimConfig(uncle_model="old", uncle_window=42).effective_uncle_window == 42 + + +def test_window_absorption_bound(): + import warnings + + with pytest.raises(ValueError): + SimConfig(window_absorption=0.5) # W < 1 rejected + with pytest.warns(RuntimeWarning, match="exceeds the spec bound"): + SimConfig(k=8, window_absorption=10.0) # W > 0.6*k warns + with warnings.catch_warnings(): + warnings.simplefilter("error") + SimConfig(k=2160, window_absorption=10.0) # full scale: silent + SimConfig(k=8, uncle_model="old", uncle_window=300) # old model: no bound def _perturb(v): @@ -140,6 +200,7 @@ def _perturb(v): "fixed": "exp", "common": "heterogeneous", "suppress": "withhold", "exp": "poisson", # jitter_dist "sine": "ramp", # churn_mode + "countable": "old", # uncle_model } if isinstance(v, str) and v in flips: return flips[v] diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py new file mode 100644 index 0000000..748516a --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py @@ -0,0 +1,84 @@ +"""Countable-model counting: measurement kernels vs the tsi.py reference oracle. + +Hand-built tree exercising every counting rule on baked references: +canonical 1(s0) -> 2(s2) -> 3(s5) -> 4(s10, tip); orphans 5(s1, parent 1, first fork), +6(s6, parent 5, DEEP), 7(s7, parent 1, first fork), 8(s7, parent 2, first fork, same slot +as 7). References: block2 -> (5,), block3 -> (1,) [a canonical block], block4 -> (6, 7, 8). + +With w = 5 and T = 20 the countable verdicts are: 5 counted (d=1); 1 skipped (on chain); +6 deep-rejected (parent is an orphan); 7 counted (d=3); 8 counted by id but its slot is +already recovered by 7 (slot dedup). Old model counts every reference. +""" + +from __future__ import annotations + +import numpy as np +import pytest + +from tsi_sim.blocktree import BlockTree +from tsi_sim.measure import measure +from tsi_sim.tsi import countable_refs, density_m + +W = 5 +T = 20 + + +def _tree() -> BlockTree: + tree = BlockTree( + slot=np.array([-1, 0, 2, 5, 10, 1, 6, 7, 7], np.int64), + parent=np.array([-1, 0, 1, 2, 3, 1, 5, 1, 2], np.int64), + height=np.array([0, 1, 2, 3, 4, 2, 3, 2, 3], np.int64), + leader=np.array([-1, 0, 1, 2, 3, 4, 5, 6, 7], np.int64), + uncles=[() for _ in range(9)], + ) + tree.uncles[2] = (5,) + tree.uncles[3] = (1,) + tree.uncles[4] = (6, 7, 8) + return tree + + +CANONICAL = [4, 3, 2, 1] +ACTIVE = np.array([0, 1, 2, 5, 6, 7, 10], np.int64) # 7 distinct active slots in T + + +def test_countable_refs_oracle(): + assert countable_refs(_tree(), CANONICAL, W) == {5, 7, 8} + + +def test_density_m_countable_and_old(): + tree = _tree() + # countable: honest slots {0,2,5,10} + recovered slots {1, 7} -> 6 + assert density_m(tree, CANONICAL, T, countable=True, w=W) == 6 + # old model: every reference counts -> recovered slots {1, 6, 7} -> 7 + assert density_m(tree, CANONICAL, T) == 7 + + +@pytest.mark.parametrize("use_numba", [False, True]) +def test_measure_countable_matches_oracle(use_numba): + tree = _tree() + A = np.zeros((2, tree.n_blocks)) # both nodes received everything + ms = measure(tree, A, ACTIVE, T, cutoff=15, use_numba=use_numba, + countable=True, w=W) + np.testing.assert_array_equal(ms.m, [6, 6]) # = density_m countable + np.testing.assert_allclose(ms.q, 4 / 7) # canonical slots / active + np.testing.assert_allclose(ms.q_eff, 6 / 7) # + recovered slots + np.testing.assert_array_equal(ms.ref_total, [5, 5]) # ids 5,1,6,7,8 examined + np.testing.assert_array_equal(ms.ref_deep, [1, 1]) # id 6 rejected as deep + + +@pytest.mark.parametrize("use_numba", [False, True]) +def test_measure_old_counts_all_refs(use_numba): + tree = _tree() + A = np.zeros((2, tree.n_blocks)) + ms = measure(tree, A, ACTIVE, T, cutoff=15, use_numba=use_numba) + np.testing.assert_array_equal(ms.m, [7, 7]) # = density_m old + np.testing.assert_allclose(ms.q_eff, 7 / 7) + np.testing.assert_array_equal(ms.ref_deep, [0, 0]) # no rule to reject on + + +def test_window_recheck_rejects_stale_reference(): + # A baked reference outside the counting window is uncounted under countable + # (the old model still counts it): shrink w below block4 -> uncle 7 distance (d=3). + tree = _tree() + assert countable_refs(tree, CANONICAL, 2) == {5} # 7, 8 now out of window (d=3) + assert density_m(tree, CANONICAL, T, countable=True, w=2) == 5 diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_slot_counting.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_slot_counting.py index aa1ca6e..a767610 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_slot_counting.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_slot_counting.py @@ -64,19 +64,31 @@ def test_distinct_slot_uncles_still_counted(): def test_zero_delay_equilibrium_is_one_not_ceiling(): - """The c(f) ceiling was the bug: corrected counting equilibrates at 1.0 with uncles.""" + """The c(f) ceiling was the bug: corrected counting equilibrates at 1.0 with uncles. + + Holds under the (default) countable model too: at zero delay the only orphans are + same-slot co-winners, which countable selection never references (occupied slot) and + which add nothing to the slot count anyway. 5 replicates / 0.02 tolerance because the + countable model's key() draws a different RNG stream than the historical runs the old + 3-rep/0.015 margin was tuned on. + """ base = dict(n_nodes=300, stake_dist="uniform", topology="full_mesh", latency=0, max_uncles=2, uncle_window=300, k=64, epochs=24, genesis_d_factor=1.0) tails = [] - for rep in range(3): + for rep in range(5): df = pd.DataFrame(run_trajectory(SimConfig(**base, replicate=rep))) tails.append(df[df.epoch >= 8].mean_ratio.mean()) - assert abs(np.mean(tails) - 1.0) < 0.015 + assert abs(np.mean(tails) - 1.0) < 0.02 def test_legacy_flag_reproduces_the_ceiling(): + # OLD model on purpose: the c(f) ceiling arises from referencing same-slot co-winners + # and counting them per block id. The countable model never references a same-slot + # co-winner (its slot is already occupied on the chain), so under it the legacy flag + # has nothing to double-count and this historical bug cannot be reproduced. base = dict(n_nodes=300, stake_dist="uniform", topology="full_mesh", latency=0, - max_uncles=2, uncle_window=300, k=64, epochs=24, genesis_d_factor=1.0) + max_uncles=2, uncle_window=300, k=64, epochs=24, genesis_d_factor=1.0, + uncle_model="old") tails = [] for rep in range(3): df = pd.DataFrame(run_trajectory( diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py index 7e8b244..4240cc8 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py @@ -45,14 +45,33 @@ def test_no_uncles_when_u_zero(): def test_window_excludes_out_of_range_orphan(): + # OLD model: uncle_window is read directly. (The countable model ignores uncle_window + # and derives the window from window_absorption — see the countable twin below.) tree, canonical = _canonical_and_orphan_tree() - cfg = SimConfig(max_uncles=1, uncle_window=1, uncle_strategy="oldest") + cfg = SimConfig(max_uncles=1, uncle_window=1, uncle_strategy="oldest", uncle_model="old") annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) # orphan 2 at slot1; nearest canonical after it is block3 at slot3 -> gap 2 > W=1 referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == set() +def test_countable_window_is_derived_from_absorption(): + # countable: w_u = round(W / f). With f=0.5 and W=1, w_u = 2 slots: the orphan at slot1 + # is out of range of the canonical block at slot5 (gap 4) and of slot3 (gap 2 <= 2 OK). + tree, canonical = _canonical_and_orphan_tree() + cfg = SimConfig(max_uncles=1, f=0.5, window_absorption=1.0) + assert cfg.effective_uncle_window == 2 + annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + referenced = {u for b in canonical for u in tree.uncles[b]} + assert referenced == {2} # block3 (slot3) still reaches it + # shrink f so the derived window rounds to 1 slot: gap 2 > 1 -> excluded + tree2, canonical2 = _canonical_and_orphan_tree() + cfg2 = SimConfig(max_uncles=1, f=0.9, window_absorption=1.0) + assert cfg2.effective_uncle_window == 1 + annotate_uncles(tree2, canonical2, cfg2, np.random.default_rng(0)) + assert {u for b in canonical2 for u in tree2.uncles[b]} == set() + + def _wide_orphan_tree(): # canonical 1(0)->6(6); orphans 2,3,4,5 at slots 1,2,3,4 (all within window of block6) tree = make_tree( @@ -108,3 +127,72 @@ def test_dedup_across_ancestors(): annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) counts = sum(len(tree.uncles[b]) for b in canonical) assert counts == 1 # orphan 2 referenced exactly once despite two eligible blocks + + +# --- countable model (spec counting rules) --------------------------------------------- + + +def _deep_fork_tree(): + # canonical 1(slot0)->5(slot5); orphan branch 2(slot1,parent=1)->3(slot2,parent=2); + # orphan 4(slot3, parent=1). Blocks 2,4 are FIRST fork blocks; 3 is deep. + tree = make_tree( + slots=[-1, 0, 1, 2, 3, 5], + parents=[-1, 0, 1, 2, 1, 1], + heights=[0, 1, 2, 3, 2, 2], + leaders=[-1, 0, 1, 2, 3, 4], + ) + return tree, [5, 1] # tip-first + + +def test_countable_excludes_deep_fork_blocks(): + tree, canonical = _deep_fork_tree() + cfg = SimConfig(max_uncles=4) + annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + referenced = {u for b in canonical for u in tree.uncles[b]} + assert referenced == {2, 4} # deep block 3 (parent is an orphan) excluded + + +def test_old_model_still_references_deep_fork_blocks(): + tree, canonical = _deep_fork_tree() + cfg = SimConfig(max_uncles=4, uncle_model="old", uncle_window=300) + annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + referenced = {u for b in canonical for u in tree.uncles[b]} + assert referenced == {2, 3, 4} # --old: fork depth ignored + + +def test_countable_excludes_occupied_slots_and_dedups_per_slot(): + # canonical 1(slot0)->5(slot4); orphans: 2 at slot0 (canonical-occupied), 3/4 at slot2. + tree = make_tree( + slots=[-1, 0, 0, 2, 2, 4], + parents=[-1, 0, 0, 1, 1, 1], + heights=[0, 1, 1, 2, 2, 2], + leaders=[-1, 0, 1, 2, 3, 4], + ) + canonical = [5, 1] + cfg = SimConfig(max_uncles=4) + annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + referenced = {u for b in canonical for u in tree.uncles[b]} + # slot0 is canonical-occupied -> orphan 2 excluded; slot2 pair -> exactly one picked + assert referenced == {3} + + +def test_production_selection_countable_rules(): + from tsi_sim.uncles import select_uncles_at_production + + # 0 genesis; 1 canonical slot0; 2 first-fork slot1 (parent 1); 3 deep slot2 (parent 2); + # 4/5 same-slot first-forks at slot3 (parent 1). + slot = np.array([-1, 0, 1, 2, 3, 3], np.int64) + parent = np.array([-1, 0, 1, 2, 1, 1], np.int64) + uncles: list = [() for _ in range(6)] + arrival = np.zeros(6) # everything arrived immediately + cfg = SimConfig(max_uncles=4) + sel = select_uncles_at_production( + slot, parent, uncles, arrival, nb=6, parent_id=1, t=5, config=cfg, + rng=np.random.default_rng(0)) + assert sel == (2, 4) # deep 3 excluded; one per slot at slot3 + + old = SimConfig(max_uncles=4, uncle_model="old", uncle_window=300) + sel_old = select_uncles_at_production( + slot, parent, uncles, arrival, nb=6, parent_id=1, t=5, config=old, + rng=np.random.default_rng(0)) + assert sel_old == (2, 3, 4, 5) # --old: depth and slot-dedup ignored From ac6a309e5816a8a8047c91168c604b5e28416844 Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Tue, 4 Aug 2026 20:48:38 +0200 Subject: [PATCH 03/22] Review fixes + high-precision design-band delay study Acts on a correctness/completeness review of the countable uncle model and its report material. Correctness fixes in the report: - s3.4 quoted 0.998 for W_abs=10 at the 8s budget; the run says 0.9963. - s1 claimed both models >= 0.996 at U >= 1; countable U=2 delta=8 is 0.9955. Corrected to >= 0.995. - The s3.2 table presented two cells (U=1 at delta 16 and 32) as model differences. They are not resolvable: t = 0.46 and 0.47 over 5 replicates. The table now carries +-SEM and a t per cell. - s3.4 claimed the ~7-block-interval floor "carries over unchanged". Accuracy is still climbing past W=7 at every delay (8s: 0.989 -> 0.996), so the claim is dropped. The 32s curve is non-monotonic with replicate SD up to 0.22 and is now flagged as noise, not a trend. - 1-r was attributed to the first-fork restriction alone; it is the combined first-fork and capacity loss, which this measurement cannot separate. Hedged to match fig32's own axis label. Completeness: the U=0 negative control was swept but never reported. With no uncles the two models are identical by construction, yet they differ by -0.23 at delta_max=32 (t=2.1) because they draw independent RNG streams. That is the noise floor the rest of the grid must clear, and it is now in s3.2, s9, fig30 and the config header. New study (configs/fine-delay.yaml, scripts/plot_fine_delay.py, s3.2a, fig34/fig35): the design band delta_max 1-5 at 40 replicates, both models. Findings: every U >= 1 cell of both models lands in 0.998-1.001, flat in delay, while U=0 decays 0.810 -> 0.640. No individual cell resolves a model difference (widest 95% CI +-0.15pp; max t=2.59 vs Bonferroni 2.94 over 15 cells). Pooled across uncle caps the first-fork cost is monotone in delay and separates from zero only at delta_max=5 (-0.0014 +- 0.0007, t=3.7) -- below 0.15% everywhere in the band, against +-0.9% per-epoch sampling noise. Code: - deep_ref_share is identically 0 on every real countable run: for a chain block B the producer's chain below B is the counting chain below B, so the counting-side parent-on-chain re-check cannot reject what selection emitted. It is a drift alarm, not a rate. Documented as such in measure.py, the plot docstring and the config header, and pinned by a new end-to-end test. - Removed annotate_uncles: a second countable implementation that production never called, while carrying most of the selection test coverage. Tests now drive select_uncles_at_production through an annotate_via_production replay helper -- same assertions, live path. - Added tests for the two previously uncovered branches of the live selection: the pmin/below chain walk that resolves parent-on-chain for candidates whose parent sits below the window, and the occupied-slot exclusion built from the chain walk. - theory.q_effective and theory.window_miss_prob were unused and untested. Now used (the prediction figure reconstructs q_u through the identity the report quotes) and tested. The window_miss_prob test records that its "~ e^-W" docstring is the f->0 limit: the true decay is e^-1.017W at f=1/30, 16% off by W=10. - Shared sem()/recovery_rate() moved into figures_pernode.py; fig30 and fig33 regenerated with SEM error bars and the U=0 control curve. - Fixed the pre-existing E501 in bootstrap_dynamics.py; ruff clean. Report prose reworked to read standalone: the countable model is described as the rules under analysis and the former model as a labelled "unrestricted" comparison baseline, with no dated banners and no round-to-round narration. Tests: 209 passed (was 202). Co-Authored-By: Claude Opus 5 (1M context) --- reports/tsi/README.md | 2 + .../report-figures/fig30_countable_vs_old.png | Bin 172481 -> 195143 bytes .../fig33_absorption_window.png | Bin 148156 -> 137625 bytes .../fig34_fine_delay_accuracy.png | Bin 0 -> 165049 bytes .../report-figures/fig35_fine_delay_gap.png | Bin 0 -> 174788 bytes ...i-report-1-overview-and-recommendations.md | 2 + .../tsi/tsi-report-2-accuracy-and-design.md | 63 +++++- ...report-4-reproducibility-and-appendices.md | 9 +- .../simulators/tsi/tsi-sim-pernode/README.md | 4 +- .../configs/countable-vs-old.yaml | 10 +- .../tsi-sim-pernode/configs/fine-delay.yaml | 35 +++ .../scripts/bootstrap_dynamics.py | 2 +- .../scripts/plot_countable_vs_old.py | 101 ++++++--- .../scripts/plot_fine_delay.py | 200 ++++++++++++++++++ .../tsi-sim-pernode/src/tsi_sim/measure.py | 16 +- .../src/tsi_sim/plotting/figures_pernode.py | 21 ++ .../tsi/tsi-sim-pernode/src/tsi_sim/uncles.py | 70 +----- .../tests/test_countable_counting.py | 25 +++ .../tsi/tsi-sim-pernode/tests/test_theory.py | 43 ++++ .../tsi/tsi-sim-pernode/tests/test_uncles.py | 105 +++++++-- 20 files changed, 585 insertions(+), 123 deletions(-) create mode 100644 reports/tsi/report-figures/fig34_fine_delay_accuracy.png create mode 100644 reports/tsi/report-figures/fig35_fine_delay_gap.png create mode 100644 tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay.yaml create mode 100644 tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py diff --git a/reports/tsi/README.md b/reports/tsi/README.md index 26f115b..fb9afd5 100644 --- a/reports/tsi/README.md +++ b/reports/tsi/README.md @@ -4,6 +4,8 @@ This report selects and justifies the TSI parameters for Cryptarchia from a per-node network simulation. It is split into four cohesive parts; section numbers (§1–§9, A–C) are stable identifiers preserved across the set. +> **Uncle references.** The model analysed throughout is the **countable** one: counting-only references, deduplicated by slot, drawn from first-fork blocks only, within a window derived as `w_u = W_abs/f`. An **unrestricted** baseline — any orphan in the window at any fork depth — is measured alongside it for comparison. The two are indistinguishable in the design regime `ρ < 1` and diverge only under overload. See the model note at the top of [Part 1](tsi-report-1-overview-and-recommendations.md), the mechanism in [§2.1](tsi-report-2-accuracy-and-design.md#s2-1), the comparison in [§3.2](tsi-report-2-accuracy-and-design.md#s3-2)–[§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a), and the reproduction notes in [§9](tsi-report-4-reproducibility-and-appendices.md#s9). + ## Parts 1. **[Overview and recommendations](tsi-report-1-overview-and-recommendations.md)** — the executive summary, the per-knob parameter reference (§7), and the safest selection with residual risks and the recommendation-vs-spec deltas (§8). diff --git a/reports/tsi/report-figures/fig30_countable_vs_old.png b/reports/tsi/report-figures/fig30_countable_vs_old.png index c8bc698c5f2e45230352ef9393c5bdf646c7c9fa..b187b75be7be609ba0d4c26b8b6141da2a4521e6 100644 GIT binary patch literal 195143 zcmeFZXIPV6*DZ<_5djqi>4-`%0@6!R6hxW`N(bp8HK9W&qEe)HsX=LC0qFz+C@pl9 zDufJIT7&oO8@E#$1sPb=2w3vYw@)qN3Bd 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z6?){cM-B{*&0}3NU2YV=_8suS(Q-hSTe@mxVn-g@s942>Soa-499c|lX@T}2t#JTn zad_lgC=tu!(cb)6*I-CNRcc$fBwZ9HpeIT(FDHOk%x=HI?khXlxRuak#*eC8O79N= z3*B-hKj&dn@*N6f{>shg%t>m{|CUN(n{T{u$D7~etw9SbT_7N#N`sBj&R?FNAl~m4 zih;h7ImF6}1G|*j7yuzhL`xT%XPpg9)nK9#3-7EOxXYw5^MTC&?=|}T3^EXcrBS3B zI~6g?WoCJk-VxO(`aE9bRStV2qW}0z6no}2S38bj5BR{lG_gfVBt>t~yUgh{iyYpV}dM(i(<(^{l&{_^qu zTBxer^M9>@CE+|{J-F+R+pZ_tnssZP88yRMI!Atj?ZurbVIJ?6Z}b7L`d8xJOYLRtCrYl^@P}=lEHAQ~SC! z*I7&B;dK{W&1WXhw9JB19iMjjyuXgiMk|<=NthtAo|L2_-<|+*>-uUIb8xPGarpBr zN0pAX;fPUW$lc>wZd0|eV z8*}q{1SiVS5}#T%JxOnI&pW@!#9lSn0f6V#z3nIw)q>ywA^vSg)W@ZeZWkxdh+L`& zHaxIm`C}Bv>dr)^TZ&R=)>V2{Bp^UxNPRE~Eh#c>9h|glk@n_P^re%tgP2g{Bag#LezaGKvmjIERM@!hLKC8yjNW*#%u z)rvFkt&2I0<`Dgru<4QI?-P0#plOXuvU*wF2^B~9{B*09NKJVw4=93_Lz0~eT zF=D7hw$%a>1+C~Y$KS<#=g`P0FT}^zTWq89(&K+-fM^cWGV|FYO)L_&-!{Wz3f4zm zKn6FkL2}Q<$QmZ~|6{ru&4Y-j6aRe_@cDni_ **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](tsi-report-2-accuracy-and-design.md#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2), [§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.25–0.45`) puts every `U ≥ 1` cell of both models in 0.998–1.001, resolves no difference in any individual cell (widest 95 % CI ±0.15 pp), and bounds the pooled first-fork cost below **0.15 %** — rising monotonically with delay and separating from zero only at the top of the band ([§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. + ## 1. Executive summary diff --git a/reports/tsi/tsi-report-2-accuracy-and-design.md b/reports/tsi/tsi-report-2-accuracy-and-design.md index 0409b30..577038e 100644 --- a/reports/tsi/tsi-report-2-accuracy-and-design.md +++ b/reports/tsi/tsi-report-2-accuracy-and-design.md @@ -48,9 +48,10 @@ D̂_next = max(1, D̂ · (1 − β·(f_p − m/T)/f_p)) β = learning rate Occupied slots more frequent than the target push the estimate up (the lottery then gets harder); less frequent pulls it down; `m/T = f_p` is the resting point. The two versions differ **only in which slots count**: - **Before uncle references (spec v1.0):** `m` counts only slots occupied by the *canonical* chain. Under Blend delay roughly a third of honest blocks are orphaned, so their slots vanish from `m`, the resting point sits far below truth (`D̂/D ≈ 0.64–0.74`, deepening with network size), and the deflated estimate makes the network *chronically over-produce* blocks at up to ~2× the target rate ([§3.2](#s3-2), fig1). Pre-uncle TSI is not viable under Blend. -- **After uncle references (spec v1.1):** `m` also counts the *referenced uncles* — orphans pointed at from the canonical chain — which puts the delay-orphaned slots back into the count and lifts the resting point up toward `D`. The spec as written deduplicates uncles by *block identity* (the same orphan referenced by two blocks counts once), recovering the bulk of the orphan loss. **This report recommends one refinement ([§8.5](tsi-report-1-overview-and-recommendations.md#s8-5)):** deduplicate by *slot*, not by block — a referenced uncle that shares a slot with a canonical block, or with another counted uncle, must add nothing. With slot-deduplication the orphaned slots return one-per-slot and the resting point lands at **exactly `D`**. +- **With uncle references, counting whole blocks (the *unrestricted* model):** `m` also counts the *referenced uncles* — orphans pointed at from the canonical chain — which puts the delay-orphaned slots back into the count and lifts the resting point up toward `D`. Any orphan in the reference window is eligible regardless of how deep in a fork it sits, and references are deduplicated by *block identity*. This report analyses it as the comparison baseline throughout, and calls it the **unrestricted** model. +- **With uncle references, counting slots under the first-fork restriction (the *countable* model — the rules analysed here):** two changes. First, deduplication is by **slot**, not by block: a referenced uncle sharing a slot with a canonical block, or with another counted uncle, adds nothing. Second, only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is what makes every reference verifiable from chain data alone (deeper fork blocks would need the fork branch's ledger state). References never affect a block's validity; they are *counting-only*, the soft-rule property the incentive analysis requires ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)). The reference window is *derived* from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k` — the `W = 10/f` sizing rule of [§3.4](#s3-4). The price of chain-only verifiability is that deep-fork orphans are unrecoverable by construction; [§3.2](#s3-2) measures what that costs, and the answer is nothing in the design regime and a bounded ceiling under overload. -So the slot-deduplicated uncle rule recovers the orphan-loss the delay caused while preserving the "one count per slot" invariant, and the recovered equilibrium is exactly 1.0 — not a ceiling above it. Counting uncle *blocks* instead — as spec v1.1 is currently written, and as an earlier version of this simulator did — double-counts same-slot co-winners (one canonical, one referenced orphan) and inflates the equilibrium by the fixed multi-winner factor `c(f) ≈ 1.017`. Every result in this report uses the corrected slot count, and [§8.5](tsi-report-1-overview-and-recommendations.md#s8-5) carries the corresponding spec recommendation; the difference is a genuine ~1.7 % accuracy bias in the deployed rule, not merely a fixed simulation bug. +Slot deduplication is what makes the recovered equilibrium exactly 1.0 rather than a ceiling above it. Counting uncle *blocks* instead double-counts same-slot co-winners (one canonical, one referenced orphan) and inflates the equilibrium by the fixed multi-winner factor `c(f) ≈ 1.017` — a genuine accuracy bias, not a simulation artefact. Every result in this report uses the slot count; where a figure or table compares the two referencing models, the unrestricted baseline is labelled as such ([§9](tsi-report-4-reproducibility-and-appendices.md#s9)). ### 2.2 The equilibrium is bounded by 1 @@ -111,10 +112,62 @@ The U = 0 under-count **deepens with N** (more nodes → more concurrent proposa ![Fig 2 — per-node D̂/D vs uncle cap U (curves: max blending delay per hop = 1/2/3 slots, averaged over N): without uncles the estimate is biased low — deeper as blending delay grows — and one uncle restores it to exactly 1.](report-figures/fig2_uncle_recovery.png) +**What the first-fork restriction costs.** Running the delay × U grid under both referencing models on the same grid (`configs/countable-vs-old.yaml`, N = 1 000, blend, 3 hops, 5 replicates; [§9](tsi-report-4-reproducibility-and-appendices.md#s9)) separates the regimes cleanly (`fig30`). Cells are replicate means ± SEM; `t` is the two-sample statistic for the countable−unrestricted gap, and cells with `t < 2` do **not** resolve a difference at this replicate count: + +| `δ_max` (s) | ρ | U | countable | unrestricted | gap (t) | +|---|---|---|---|---|---| +| 4 | ≈ 0.4 | 1 / 2 / 4 | 0.9979 ± 0.0015 / 0.9982 ± 0.0014 / 0.9995 ± 0.0012 | 0.9981 ± 0.0006 / 0.9985 ± 0.0012 / 0.9992 ± 0.0013 | *none resolved* (0.1–0.2) | +| 8 | ≈ 0.6 | 1 / 2 / 4 | 0.9965 ± 0.0015 / 0.9955 ± 0.0017 / 0.9963 ± 0.0015 | 0.9986 ± 0.0017 / 0.9993 ± 0.0016 / 0.9989 ± 0.0017 | *none resolved* (1.0–1.6) | +| 16 | ≈ 1.0 | 1 | 0.9647 ± 0.0065 | 0.9610 ± 0.0043 | *not resolved* (0.5) | +| 16 | ≈ 1.0 | 2 / 4 | 0.9862 ± 0.0010 / 0.9911 ± 0.0032 | 0.9999 ± 0.0005 / 1.0013 ± 0.0011 | −0.014 (12.1) / −0.010 (3.0) | +| 32 | ≈ 1.8 | 1 | 0.608 ± 0.069 | 0.570 ± 0.042 | *not resolved* (0.5) | +| 32 | ≈ 1.8 | 2 / 4 | 0.9343 ± 0.0015 / 0.9517 ± 0.0007 | 0.9774 ± 0.0064 / 1.0020 ± 0.0010 | −0.043 (6.5) / −0.050 (41.0) | + +**The `U = 0` rows are a negative control.** With no uncles the two models are identical by construction — no reference is ever taken, so any measured gap is pure between-run noise (the two models draw independent RNG streams by design, so the comparison is unpaired). That control reads **+0.010 (t = 0.8) at `δ_max = 4`** but **−0.230 (t = 2.1) at `δ_max = 32`**, where single replicates range from 0.05 to 0.60. Read the table against that floor: at `δ_max = 32` a gap must clear ~0.2 to mean anything on a single-replicate basis, which is exactly why the `U = 1` cells there are reported as unresolved while the tightly-clustered `U = 2` and `U = 4` cells are not. + +So: **at the operating loads (`ρ < 1`) no difference between the models is detectable at all** — the first-fork restriction costs nothing measurable where forks are shallow, and both models sit at ≥ 0.995 for every `U ≥ 1`. ([§3.2a](#s3-2a) puts a much tighter bound on this region.) Differences appear only at `ρ ≥ 1` and only at `U ≥ 2`: at `ρ ≈ 1` the restriction trims ~1.4 %, and in overload the countable recovery **saturates** — raising `U` 2 → 4 buys only 0.934 → 0.952 while the unrestricted model reaches ~1.00. The ceiling is the measured recovery rate `r` (0.92 at `δ_max = 32`, `U = 4`), set by the fork-*depth* profile rather than by capacity, so no uncle cap buys it back. The closed form `D̂/D = log(1−f)/log(1−f/q_u)` with the measured `q_u = q + (1−q)·r` predicts every countable cell to within 0.2 % (`fig31`). + +`fig32` shows `r` and the residual `1−r` per delay, rising from 0.3 % to 7.8 % of the waste as `δ_max` goes 4 → 32 at `U = 4`. That residual is the *combined* first-fork and capacity loss — the simulator cannot separate the two, because the restriction acts at selection (a deep orphan is simply never referenced) rather than at counting. At `U = 4`, where capacity is not binding for `ρ ≤ 1.8`, most of it is attributable to fork depth; the split is not measured directly. + +![Fig 30 — equilibrium D̂/D vs Blend mixing delay, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM. The U=0 pair is the negative control: the models are identical with no uncles, so the visible gap there — small at low delay, large at 32 — is the pure between-run noise floor. Countable saturates below 1 in overload, where deep forks are unrecoverable by construction.](report-figures/fig30_countable_vs_old.png) + +![Fig 31 — the q→q_u reduction check: predicted log(1−f)/log(1−f/q̄_u) from the measured q̄_u vs the simulated equilibrium, all countable U≥1 cells on the diagonal within 0.2 %.](report-figures/fig31_countable_prediction.png) + +![Fig 32 — measured recovery rate r (left) and the non-recovered waste share 1−r on a log axis (right) vs mixing delay: near-total recovery at design loads; the residual — first-fork and capacity losses combined, which this measurement cannot separate — grows with delay.](report-figures/fig32_countable_recovery.png) + **Bootstrap is self-limiting — but only with uncles** (`fig1`; full scale, k = 2160, Blend, N = 1 000 and 5 000, genesis guesses 0.01×–2× the true stake; 0.1×–2× at N = 5 000). With uncles (U = 2, solid lines) the cold start is a non-event: whatever the guess, block production snaps back to the target `f` within ~2–2.5 epochs and the estimate lands on 1.0 by epoch 2 — identically at both network sizes. Without uncles (U = 0, dashed) the system also converges from any guess, **but to the wrong place**: the estimate settles below truth (mean ≈ 0.58× across guesses, ranging ≈0.48–0.85; ≈0.51× at N = 5 000) and the network then *chronically over-produces* blocks at ~1.85× the target rate (~2.0× at N = 5 000) — the [§6.2](tsi-report-3-robustness-and-incentives.md#s6-2) load feedback in the flesh (a low estimate makes the lottery easier, extra blocks orphan, the count stays low). So uncle references are load-bearing from the very first epochs: they are what makes the bootstrap end *at the truth* rather than at a permanently overheated equilibrium. ![Fig 1 — bootstrap at full scale (k=2160, Blend, N=1000): from any genesis guess (0.01×–2×), with uncles (solid, U=2) block production (top) and the estimate (bottom) converge to the target f and D̂/D = 1.0 within ~2–3 epochs (≈2 from a near-correct guess, ~3 from the extreme 0.01× start); without uncles (dashed, U=0) they settle more slowly to a chronically overheated, guess-dependent equilibrium — D̂/D ≈ 0.48–0.85 (mean ≈ 0.58; ≈ 0.51 at N=5000), block rate ≈ 1.2–2.1×f.](report-figures/fig1_bootstrap.png) + +### 3.2a The design band at high precision — `δ_max` 1–5 + +**The question.** [§3.2](#s3-2) samples the mixing delay at 4/8/16/32. That resolves the overload regime, but it leaves the band the parameters are actually chosen in — the low-delay end, where every operating point sits — measured at four-fold spacing and five replicates, which is enough to say "no difference detected" and nothing more. How accurate is TSI across `δ_max` = 1–5, and how large a first-fork cost can be *excluded* there? + +**The finding.** With one uncle slot the estimate is exact across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay. Without uncles the same band decays steeply, 0.810 → 0.640. Through `δ_max ≤ 4` the two referencing models are **indistinguishable**, and the first-fork restriction begins to cost something measurable only at the top of the band. + +`configs/fine-delay.yaml` spends replicates instead of range — `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, **40 replicates** per cell (8× [§3.2](#s3-2)), N = 1 000, blend, 3 hops — run under both models ([§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The band spans `ρ ≈ 0.25` to `0.45`, entirely inside the design regime. + +| `δ_max` (s) | ρ | `U=0` countable / unrestricted | `U≥1` countable | `U≥1` unrestricted | pooled gap (t) | +|---|---|---|---|---|---| +| 1 | ≈ 0.25 | 0.810 / 0.806 | 0.9994 – 0.9999 | 0.9990 – 1.0010 | −0.0004 ± 0.0007 (1.1) | +| 2 | ≈ 0.30 | 0.762 / 0.763 | 0.9996 – 1.0002 | 0.9996 – 1.0003 | +0.0000 ± 0.0008 (0.0) | +| 3 | ≈ 0.35 | 0.716 / 0.723 | 0.9995 – 1.0002 | 0.9992 – 1.0004 | −0.0001 ± 0.0008 (0.2) | +| 4 | ≈ 0.40 | 0.664 / 0.668 | 0.9988 – 0.9996 | 0.9995 – 0.9999 | −0.0005 ± 0.0008 (1.3) | +| 5 | ≈ 0.45 | 0.640 / 0.623 | 0.9982 – 0.9988 | 0.9995 – 1.0003 | **−0.0014 ± 0.0007 (3.7)** | + +**No individual cell resolves a model difference.** Across the 15 `U ≥ 1` cells the widest 95 % CI half-width is ±0.0015, one cell clears `t = 2` (0.75 are expected to by chance), and its `t = 2.59` does not survive the Bonferroni threshold of 2.94 for 15 tests. Read cell by cell, the honest statement is that any difference is **smaller than ±0.15 pp**. + +**Pooled, a small delay-dependent cost appears.** The three uncle caps are independent measurements of the same underlying difference, so inverse-variance pooling across them buys ~√3 in precision. Pooled per delay, `δ_max` 1–4 stay unresolved (|t| ≤ 1.3) while **`δ_max = 5` resolves at −0.0014 ± 0.0007 (t = 3.7)** — surviving correction for the five delays tested. Over the whole band the pooled gap is −0.00048 ± 0.00033 (t = 2.8), and 11 of 15 cells are negative. So the first-fork restriction does cost something, in the direction theory predicts, and the cost is **monotone in delay and below 0.15 % everywhere in this band** — negligible against the ±0.9 % per-epoch sampling noise of [Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB). (The pooling was chosen after inspecting the per-cell results; the per-delay trend, not the whole-band figure, is the defensible claim.) + +**The negative control passes.** The `U = 0` arms — identical models by construction — show |gap| ≤ 0.016 with max `t` = 1.26, i.e. no spurious signal, but a 95 % CI of ±0.025: **17× wider than the entire `U ≥ 1` range.** The unrecovered regime is intrinsically noisy, which is precisely why the model comparison has to be made where uncles are active. + +![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM over 40 replicates: every U ≥ 1 curve is pinned at 1.000 across the band under both models, while U = 0 (the negative control) decays 0.81 → 0.64.](report-figures/fig34_fine_delay_accuracy.png) + +![Fig 35 — the countable − unrestricted gap with 95% CIs, zoomed to the U ≥ 1 scale, with the inverse-variance pooled estimate in black: no single cell resolves, the pooled trend is monotone in delay, and only δ_max = 5 separates from zero (−0.0014 ± 0.0007).](report-figures/fig35_fine_delay_gap.png) + +**What this settles.** One uncle slot is sufficient — not approximately, exactly — everywhere in the operating band, under either referencing model; the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.45`. And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **less than 0.15 %** anywhere a deployment should be operating. + ### 3.3 One uncle is not always enough — the load `ρ` @@ -183,6 +236,12 @@ So the two levers separate cleanly: **`U` must cover the average load; `W` must ![Fig 25 — window sufficiency at scale (N = 1 000 blue vs N = 10 000 orange; U = 1 solid circles / U = 2 dashed squares): the floor position is N-invariant (left), W = 600 buys back the ρ ≈ 1 boundary (middle), and no window fixes ρ > U (right).](report-figures/fig25_window_scale.png) +**The derived window.** Sweeping the *derived* window `w_u = W_abs/f` directly (`configs/absorption-window.yaml`, U = 1, 5 replicates; `fig33`) confirms the `10/f` margin, with one correction to the shape. At the 8-s budget recovery runs 0.709 → 0.940 → **0.996** as `W_abs` goes 1 → 3 → 10; at the 16-s budget (`ρ ≈ 1`) `W_abs = 10` reaches 0.964; at the 32-s budget no window recovers what `U = 1` cannot drain. The window-miss probability `(1−f)^(W_abs/f)` falls below 10⁻⁴ by `W_abs = 10`, so past that point the window is no longer a loss channel — which is what makes `W_abs = 10` and the bound `W_abs ≤ 0.6·k` land on this section's `W = 10/f` rule. + +Two cautions on reading `fig33`. **Accuracy has not saturated at `W_abs ≈ 7`** — it is still climbing at every delay (8 s: 0.989 → 0.996; 16 s: 0.942 → 0.964 from 7 to 10), so the ≈ 7-block-interval queueing floor of the raw-slot sweep above is a floor on *usefulness*, not a point where widening stops paying. And the **32-s curve is noise, not a trend**: replicate SD reaches 0.22 there and the sampled points are non-monotonic (0.623 at `W_abs = 5`, 0.526 at 7, 0.617 at 10). Only its ceiling is meaningful, and that ceiling is set by `U = 1`, not by the window. + +![Fig 33 — accuracy vs the window absorption parameter W_abs (derived w_u = W_abs/f) at U=1 for three mixing delays, error bars = replicate SEM: the spec default W_abs=10 recovers essentially fully at design loads and is still climbing at 7; the overloaded 32-s curve is U-limited and dominated by run-to-run spread, so its shape carries no signal.](report-figures/fig33_absorption_window.png) + ### 3.5 The joint (W, U) region — the levers are hierarchical diff --git a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md index fa24591..473701b 100644 --- a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md +++ b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md @@ -45,10 +45,17 @@ Sweep studies are committed configs, run with `make ` (writes a dated `run | soft uncle inclusion (reward share vs emergent `p_ref`) | `scripts/reward_mandate.py` | [§6.8](tsi-report-3-robustness-and-incentives.md#s6-8), [§6.9](tsi-report-3-robustness-and-incentives.md#s6-9) | | U = 0 fluctuation series (zero delay, k ∈ {256, 1024, 2160}) | `scripts/appendix_fluct.py --run` (`runs/fluctuation_u0.parquet`) | [Appendix B](#sB) | | CI smoke grid + analytic sanity checks | `configs/smoke.yaml`; `scripts/verify.py` (`make verify`) — validation only, no figures | — | +| **countable vs unrestricted referencing** (accuracy over delay × U; measured `q_u`/recovery `r`) | `configs/countable-vs-old.yaml` run twice — default and with `--old`; figures + significance table by `scripts/plot_countable_vs_old.py` | [§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) | +| **fine delay band** (δ_max 1–5 at 40 replicates; tight CI on the model gap in the design regime) | `configs/fine-delay.yaml` run twice — default and with `--old`; figure + table by `scripts/plot_fine_delay.py` | [§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a) | +| **window absorption sweep** (`W` in expected block-intervals, `w_u = W/f` derived) | `configs/absorption-window.yaml`; figure by `scripts/plot_countable_vs_old.py` | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | + +**Uncle-model convention.** The simulator's default is the **countable** model — first-fork candidates only, derived window `w_u = W/f`, occupied-slot exclusion, per-reference counting rules ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)). The **unrestricted** baseline is preserved in the code and selected with `--old` on `tsi-sweep`/`tsi-verify`. Its RNG key is byte-identical to the pre-restriction key, so `--old` **bit-reproduces the earlier runs**: a `rho-boundary` cell (δ_max = 8, U = 2, k = 256, N = 1 000) re-run under `--old` matches the committed `2026-07-27_195627_rho-boundary` parquet with `max |Δ| = 0` on every epoch and every metric. Studies in the table above that predate the countable default were produced under the unrestricted model and reproduce exactly under `--old`; the comparison rows quantify where the two models differ, and in the design regime (`ρ < 1`) no difference is resolvable, so those findings carry over unchanged. + +Because the two models draw independent RNG streams, every countable-vs-unrestricted comparison is **unpaired**, and its resolution is set by the replicate spread rather than by the effect size. Each comparison sweep therefore includes a `U = 0` arm as a **negative control**: with no uncles the models are identical by construction, so the measured `U = 0` gap is a direct reading of the noise floor at that delay and replicate count. At `δ_max = 32` with 5 replicates that floor is ≈ 0.23 in `D̂/D` — larger than several real effects elsewhere in the grid — which is why [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) reports a `t` statistic per cell and why the design regime is measured separately at 40 replicates ([§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a)). All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. -Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` (block-rate `U_min` grid + ρ-collapse) rendered ad hoc from `runs/2026-07-24_043943_block-rate` with no committed generator; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` pool both sizes in that run, N = 5 000 and N = 10 000 — the generators filter on stake_dist/topology/degree/init_dest only, never on `n_nodes`); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). +Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` (block-rate `U_min` grid + ρ-collapse) rendered ad hoc from `runs/2026-07-24_043943_block-rate` with no committed generator; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` pool both sizes in that run, N = 5 000 and N = 10 000 — the generators filter on stake_dist/topology/degree/init_dest only, never on `n_nodes`); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay; `fig30`–`fig33` (countable-vs-unrestricted accuracy, `q_u`-prediction check, recovery rate, absorption-window sweep) by `scripts/plot_countable_vs_old.py` from the `cvo-countable`/`cvo-old`/`absorption-window` runs; `fig34`–`fig35` (design-regime accuracy and the model gap with 95 % CIs) by `scripts/plot_fine_delay.py` from the `fine-countable`/`fine-old` runs. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). --- diff --git a/tools/simulators/tsi/tsi-sim-pernode/README.md b/tools/simulators/tsi/tsi-sim-pernode/README.md index 9acf057..fac1903 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/README.md +++ b/tools/simulators/tsi/tsi-sim-pernode/README.md @@ -156,7 +156,9 @@ src/tsi_sim/ constants config rng stake lottery topology blocktree(+build_tree theory verify plotting/{style, figures_pernode, make_figures} configs/ smoke.yaml default.yaml fullscale.yaml countable-vs-old.yaml absorption-window.yaml (countable-model studies) + fine-delay.yaml (delay 1-5 at 40 replicates: the design band, high precision) tests/ test_{pernode,config,rng,lottery,blocktree,uncles,tsi_counting,stake, theory,latency,theory_convergence,countable_counting,...}.py -scripts/ plot_countable_vs_old.py (old-vs-countable comparison figures) +scripts/ plot_countable_vs_old.py (countable-vs-unrestricted comparison figures) + plot_fine_delay.py (design-band accuracy + model gap with 95% CIs) ``` diff --git a/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml b/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml index 3bdd5d6..ce4f71d 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml +++ b/tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old.yaml @@ -1,8 +1,12 @@ # Headline comparison for the countable uncle model (cryptarchia-v1-protocol.md counting # rules) vs the old pre-redesign model: accuracy vs Blend mixing delay at U in {0,1,2,4}. -# Run TWICE — default (countable) and with --old — same grid; the countable run also -# yields deep_ref_share (the first-fork restriction's rejection rate) and q/q_eff for the -# q_u = q + (1-q) r theory overlay. Latency is in SLOTS (1 slot = 1 s). +# Run TWICE — default (countable) and with --old — same grid; the countable run yields +# q/q_eff for the q_u = q + (1-q) r theory overlay. (deep_ref_share is a drift alarm that +# reads 0 on every real run, NOT a measured rejection rate — see measure.py.) The U=0 rows +# are the NEGATIVE CONTROL: with no uncles the two models are identical by construction, so +# any U=0 gap is pure between-run RNG noise (the models draw different streams by design) +# and bounds what a real countable-vs-old effect must exceed. +# Latency is in SLOTS (1 slot = 1 s). n_nodes: [1000] # network size stake_dist: [pareto] # heavy-tailed (realistic) stake distribution topology: [blend] # Blend mixnet (the multi-slot fork regime) diff --git a/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay.yaml b/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay.yaml new file mode 100644 index 0000000..e801234 --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay.yaml @@ -0,0 +1,35 @@ +# High-precision sweep of the LOW mixing-delay region — the intended operating band. +# +# countable-vs-old.yaml samples delay at 4/8/16/32 with 5 replicates, which resolves the +# overload regime but leaves the design regime under-measured: at delay <= 8 every +# countable-vs-old gap there sits inside the replicate noise, so the report can only say +# "no difference detected", not how large a difference is excluded. This sweep spends the +# replicates instead of the range — delay 1..5 at 40 replicates — to put a tight CI on the +# model difference exactly where the parameters are actually chosen. +# +# rho = f * D_vis with D_vis = hops*delta_max/2 + (hops+1)*ell_mean spans ~0.25 (delay 1) +# to ~0.45 (delay 5), so the whole sweep sits well inside rho < 1 and U >= 1 should hold +# the equilibrium at 1.0 under BOTH models. The question is the size of the residual gap. +# +# Run TWICE — default (countable) and with --old — same grid. U=0 is the negative control: +# with no uncles the models are identical by construction, so the U=0 gap measures the +# between-run RNG noise floor at this replicate count and bounds what a real effect must +# exceed. Latency is in SLOTS (1 slot = 1 s). +n_nodes: [1000] # network size +stake_dist: [pareto] # heavy-tailed (realistic) stake distribution +topology: [blend] # Blend mixnet (the multi-slot fork regime) +degree: [6] # peering degree of the d-regular graph +link_latency_mean: [0.5] # natural geographic transport (sub-slot) +link_latency_dist: [geo] # real-world geographic band mixture +blend_hops: [3] # fixed hop count; delay is the swept knob +blend_delay_max: [1.0, 2.0, 3.0, 4.0, 5.0] # THE fine region (integer slots) +max_uncles: [0, 1, 2, 4] # U: 0 = negative control, then the levers +uncle_strategy: [oldest] # spec selection: oldest-first fill +init_dest: [common] # per-node initial D_est from agreement +replicates: 40 # 8x countable-vs-old.yaml: this is the point +base: # per-run settings shared by every cell + k: 2160 # true security parameter + epochs: 20 # equilibrium within ~2 epochs; burn 50% + f: 0.03333333333333333 # slot activation coefficient (1/30) + genesis_d_factor: 0.5 # start near true stake (cheap epoch 0) + early_stop: true diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py index 09455af..e35e308 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/bootstrap_dynamics.py @@ -54,7 +54,7 @@ def fig1(df: pd.DataFrame) -> None: # Both panels are indexed by the estimate that DROVE each epoch's production: the # start-of-epoch estimate `mean_ratio_in` (block rate depends on it, and at epoch 0 it # IS the genesis guess, matching the legend). Plotting end-of-epoch `mean_ratio` here - # would show the already-updated value at epoch 0 and offset the two panels by one epoch. + # would show the already-updated value at epoch 0 and offset the panels by one epoch. s = (d[(d.gdf == gdf) & (d.u == u)] .groupby("epoch").agg(rate=("n_blocks", "mean"), ratio=("mean_ratio_in", "mean"))) rate = s.rate / (10 * int(2160 / F)) # blocks per slot diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py index 77b32c4..db3273a 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_countable_vs_old.py @@ -12,8 +12,11 @@ and renders (into --out): dashed = old, one Okabe-Ito hue per U (color follows U). cvo_prediction_vs_sim predicted log(1-f)/log(1-f/q_u) from the MEASURED q_u vs the simulated equilibrium — the q -> q_u reduction check. - cvo_recovery_vs_delay measured recovery r = (q_eff - q)/(1 - q) and the first-fork - rejection share (deep_ref_share) vs delay. + cvo_recovery_vs_delay measured recovery r = (q_eff - q)/(1 - q) and the non-recovered + waste share 1-r vs delay. (NOT deep_ref_share: under joint + countable selection+counting that is identically 0 — the + first-fork restriction acts at selection, so it shows up + inside 1-r alongside capacity losses.) absorption_window equilibrium vs the window absorption parameter W per delay. Usage: @@ -31,8 +34,8 @@ import numpy as np import pandas as pd from tsi_sim.plotting import style -from tsi_sim.plotting.figures_pernode import equilibrium -from tsi_sim.theory import expected_ratio +from tsi_sim.plotting.figures_pernode import equilibrium, recovery_rate, sem +from tsi_sim.theory import expected_ratio, q_effective DELAY = "blend_delay_max" @@ -42,37 +45,56 @@ def _load(run_dir: str | Path) -> pd.DataFrame: def _eq(df: pd.DataFrame, extra_cols: tuple[str, ...] = ()) -> pd.DataFrame: - """Equilibrium (post-burn) means per (delay, U) cell, averaged over replicates.""" + """Equilibrium (post-burn) per (delay, U) cell: replicate mean, SEM and count. + + ``equilibrium`` returns one row per (config, replicate); the spread across those + replicates is the only uncertainty estimate available, and at high delay it is large + enough to swamp the model difference — so every consumer here carries it. + """ eq = equilibrium(df) keys = [DELAY, "max_uncles", *extra_cols] - agg = {"mean_ratio": "mean", "mean_q": "mean", "mean_q_eff": "mean"} - if "deep_ref_share" in eq.columns: - agg["deep_ref_share"] = "mean" - return eq.groupby(keys, as_index=False).agg(agg) + agg = {"mean_ratio": ("mean_ratio", "mean"), + "sem_ratio": ("mean_ratio", sem), + "n_rep": ("mean_ratio", "size"), + "mean_q": ("mean_q", "mean"), + "mean_q_eff": ("mean_q_eff", "mean")} + return eq.groupby(keys, as_index=False).agg(**agg) def fig_accuracy_vs_delay(cnt: pd.DataFrame, old: pd.DataFrame) -> plt.Figure: - fig, ax = plt.subplots() + """Accuracy vs delay per U, with replicate SEM bars. + + U=0 is the NEGATIVE CONTROL: with no uncles the two models are identical by + construction, so the visible countable-vs-old gap on that pair of curves is pure + between-run RNG noise and calibrates what a real difference has to beat. + """ + fig, ax = plt.subplots(figsize=(6.4, 4.2)) us = sorted(cnt["max_uncles"].unique()) for i, u in enumerate(us): c = style.color_for(i) a = cnt[cnt.max_uncles == u].sort_values(DELAY) b = old[old.max_uncles == u].sort_values(DELAY) - ax.plot(a[DELAY], a.mean_ratio, "-o", color=c, label=f"U={u} countable", ms=4) - ax.plot(b[DELAY], b.mean_ratio, "--s", color=c, label=f"U={u} old", ms=4, - alpha=0.75) + ctl = " (control)" if u == 0 else "" + ax.errorbar(a[DELAY], a.mean_ratio, yerr=a.sem_ratio, fmt="-o", color=c, + label=f"U={u} countable{ctl}", ms=4, capsize=2, lw=1.2) + ax.errorbar(b[DELAY], b.mean_ratio, yerr=b.sem_ratio, fmt="--s", color=c, + label=f"U={u} unrestricted{ctl}", ms=4, capsize=2, alpha=0.75, lw=1.2) ax.axhline(1.0, color="0.4", lw=0.8, ls=":") ax.set_xlabel("max per-relay mixing delay (slots)") ax.set_ylabel(r"equilibrium $\hat{D}/D_{true}$") - ax.set_title("Accuracy vs delay: countable (solid) vs old (dashed) uncle model") - ax.legend(ncol=2) + ax.set_title("Accuracy vs delay: countable (solid) vs unrestricted (dashed) referencing") + ax.legend(ncol=2, fontsize="x-small") return fig def fig_prediction_vs_sim(cnt: pd.DataFrame, f: float) -> plt.Figure: fig, ax = plt.subplots(figsize=(4.6, 4.4)) sub = cnt[cnt.max_uncles > 0] - pred = expected_ratio(f, sub.mean_q_eff.to_numpy()) + # Reconstruct q_u through the theory identity the report quotes, q_u = q + (1-q) r, + # rather than reading mean_q_eff straight off the parquet: the figure then exercises + # the same closed form the text claims. + r = recovery_rate(sub.mean_q.to_numpy(), sub.mean_q_eff.to_numpy()) + pred = expected_ratio(f, q_effective(sub.mean_q.to_numpy(), r)) us = sorted(sub["max_uncles"].unique()) for i, u in enumerate(us): m = (sub.max_uncles == u).to_numpy() @@ -96,8 +118,7 @@ def fig_recovery_vs_delay(cnt: pd.DataFrame) -> plt.Figure: us = [u for u in sorted(cnt["max_uncles"].unique()) if u > 0] for i, u in enumerate(us): a = cnt[cnt.max_uncles == u].sort_values(DELAY) - denom = np.maximum(1.0 - a.mean_q.to_numpy(), 1e-12) - r = (a.mean_q_eff.to_numpy() - a.mean_q.to_numpy()) / denom + r = recovery_rate(a.mean_q.to_numpy(), a.mean_q_eff.to_numpy()) ax1.plot(a[DELAY], r, "-o", color=style.color_for(i), label=f"U={u}", ms=4) ax2.semilogy(a[DELAY], np.maximum(1.0 - r, 1e-4), "-o", color=style.color_for(i), label=f"U={u}", ms=4) @@ -114,13 +135,20 @@ def fig_recovery_vs_delay(cnt: pd.DataFrame) -> plt.Figure: def fig_absorption_window(absw: pd.DataFrame) -> plt.Figure: - fig, ax = plt.subplots() + """Accuracy vs the derived window, with replicate SEM bars. + + The bars matter here: at the 32-slot delay the run-to-run spread is the dominant + feature (replicate sd up to ~0.22), so that curve's shape is not interpretable as a + trend — only its ceiling is, and the ceiling is set by U=1, not by the window. + """ + fig, ax = plt.subplots(figsize=(6.0, 4.0)) eq = equilibrium(absw) - agg = eq.groupby([DELAY, "window_absorption"], as_index=False).mean_ratio.mean() + agg = eq.groupby([DELAY, "window_absorption"], as_index=False).agg( + mean_ratio=("mean_ratio", "mean"), sem_ratio=("mean_ratio", sem)) for i, d in enumerate(sorted(agg[DELAY].unique())): a = agg[agg[DELAY] == d].sort_values("window_absorption") - ax.plot(a.window_absorption, a.mean_ratio, "-o", color=style.color_for(i), - label=f"delay={d:g}", ms=4) + ax.errorbar(a.window_absorption, a.mean_ratio, yerr=a.sem_ratio, fmt="-o", + color=style.color_for(i), label=f"delay={d:g}", ms=4, capsize=2, lw=1.2) ax.axhline(1.0, color="0.4", lw=0.8, ls=":") ax.set_xlabel("window absorption parameter W (expected block-intervals)") ax.set_ylabel(r"equilibrium $\hat{D}/D_{true}$") @@ -151,17 +179,32 @@ def main() -> None: written += style.save(fig_recovery_vs_delay(cnt), out / "cvo_recovery_vs_delay", prov) written += style.save(fig_absorption_window(_load(args.absorption)), out / "absorption_window", prov) - # headline numbers for the report / analysis doc + # Headline numbers for the report. Every countable-vs-old gap is printed with the + # two-sample t = |diff| / SE(diff) over replicates; |t| < 2 means the cell does NOT + # resolve a model difference at this replicate count and must not be read as one. + # The U=0 rows are the negative control (models identical by construction, so their + # t is a pure noise reading). + print(f"{'cell':<14} {'countable':>17} {'old':>17} {'diff':>9} {'t':>6} verdict") for u in sorted(cnt["max_uncles"].unique()): for _, row in cnt[cnt.max_uncles == u].sort_values(DELAY).iterrows(): q, qu = row.mean_q, row.mean_q_eff - r = (qu - q) / max(1.0 - q, 1e-12) + r = float(recovery_rate(q, qu)) o = old[(old.max_uncles == u) & (old[DELAY] == row[DELAY])] - old_ratio = float(o.mean_ratio.iloc[0]) if len(o) else float("nan") - print(f"U={u} delay={row[DELAY]:>5g} countable={row.mean_ratio:.4f} " - f"old={old_ratio:.4f} q={q:.4f} q_u={qu:.4f} r={r:.4f} " - f"pred={float(expected_ratio(f, qu)):.4f} " - f"deep={row.get('deep_ref_share', float('nan')):.4f}") + if not len(o): + continue + orow = o.iloc[0] + diff = row.mean_ratio - orow.mean_ratio + se = float(np.hypot(row.sem_ratio, orow.sem_ratio)) + t = abs(diff) / se if se > 0 else float("inf") + verdict = ("CONTROL (must be 0)" if u == 0 else + "resolved" if t >= 2 else "NOT RESOLVED (noise)") + print(f"U={u} delay={row[DELAY]:>5g} " + f"{row.mean_ratio:.4f}+-{row.sem_ratio:.4f} " + f"{orow.mean_ratio:.4f}+-{orow.sem_ratio:.4f} " + f"{diff:+.4f} {t:6.2f} {verdict}") + print(f"{'':>14} q={q:.4f} q_u={qu:.4f} r={r:.4f} " + f"pred={float(expected_ratio(f, q_effective(q, r))):.4f} " + f"n_rep={int(row.n_rep)}") print(f"wrote {len(written)} files -> {out}") diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py new file mode 100644 index 0000000..5bfd32c --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py @@ -0,0 +1,200 @@ +"""High-precision figures for the LOW mixing-delay band (the design regime). + +countable-vs-old.yaml samples delay at 4/8/16/32 with 5 replicates. That resolves the +overload regime but leaves the design regime under-measured: every countable-vs-unrestricted +gap at delay <= 8 sits inside the replicate noise there, so the only honest statement is +"no difference detected" — with no bound on how large an undetected difference could be. + +fine-delay.yaml spends replicates instead of range (delay 1..5, 40 replicates) to turn that +into a real bound. Consumes: + + tsi-sweep --config configs/fine-delay.yaml --label fine-countable + tsi-sweep --config configs/fine-delay.yaml --old --label fine-old + +and renders (into --out): + + fine_accuracy_vs_delay equilibrium D/D_true vs delay 1..5, countable (solid) vs + unrestricted (dashed) per U, replicate-SEM bars. + fine_gap_vs_delay THE precision figure: the countable - unrestricted gap with 95% + CIs, against the U=0 negative-control band. A CI straddling zero + means no difference at this power; the band shows the floor. + +Usage: + python scripts/plot_fine_delay.py --countable RUNDIR --old RUNDIR \ + --out figures/fine-delay +""" + +from __future__ import annotations + +import argparse +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +from tsi_sim.plotting import style +from tsi_sim.plotting.figures_pernode import equilibrium, sem + +DELAY = "blend_delay_max" +# Normal approximation: with 40 replicates per arm the t-quantile is within ~2% of 1.96, +# and the replicate spread itself is the dominant uncertainty, so 1.96 is precise enough. +Z95 = 1.96 + + +def _load(run_dir: str | Path) -> pd.DataFrame: + return pd.read_parquet(Path(run_dir) / "results.parquet") + + +def _cells(df: pd.DataFrame) -> pd.DataFrame: + """Per (delay, U): replicate mean, SEM and count of the equilibrium accuracy.""" + return equilibrium(df).groupby([DELAY, "max_uncles"], as_index=False).agg( + mean_ratio=("mean_ratio", "mean"), + sem_ratio=("mean_ratio", sem), + n_rep=("mean_ratio", "size"), + mean_q=("mean_q", "mean"), + mean_q_eff=("mean_q_eff", "mean")) + + +def gaps(cnt: pd.DataFrame, old: pd.DataFrame) -> pd.DataFrame: + """countable - unrestricted per cell, with the unpaired SE and 95% CI half-width.""" + m = cnt.merge(old, on=[DELAY, "max_uncles"], suffixes=("_c", "_o")) + m["gap"] = m.mean_ratio_c - m.mean_ratio_o + m["se"] = np.hypot(m.sem_ratio_c, m.sem_ratio_o) + m["ci95"] = Z95 * m.se + m["t"] = np.where(m.se > 0, np.abs(m.gap) / m.se.replace(0, np.nan), np.inf) + return m.sort_values(["max_uncles", DELAY]) + + +def fig_accuracy(cnt: pd.DataFrame, old: pd.DataFrame) -> plt.Figure: + fig, ax = plt.subplots(figsize=(6.4, 4.2)) + for i, u in enumerate(sorted(cnt["max_uncles"].unique())): + c = style.color_for(i) + a = cnt[cnt.max_uncles == u].sort_values(DELAY) + b = old[old.max_uncles == u].sort_values(DELAY) + ctl = " (control)" if u == 0 else "" + ax.errorbar(a[DELAY], a.mean_ratio, yerr=a.sem_ratio, fmt="-o", color=c, + label=f"U={u} countable{ctl}", ms=4, capsize=2, lw=1.2) + ax.errorbar(b[DELAY], b.mean_ratio, yerr=b.sem_ratio, fmt="--s", color=c, + label=f"U={u} unrestricted{ctl}", ms=4, capsize=2, alpha=0.75, lw=1.2) + ax.axhline(1.0, color="0.4", lw=0.8, ls=":") + ax.set_xlabel("max per-relay mixing delay (slots)") + ax.set_ylabel(r"equilibrium $\hat{D}/D_{true}$") + ax.set_title("Design-regime accuracy: countable vs unrestricted referencing") + ax.legend(ncol=2, fontsize="x-small") + return fig + + +def pooled_by_delay(g: pd.DataFrame) -> pd.DataFrame: + """Inverse-variance pooled gap across the U >= 1 arms, per delay. + + Individual cells are underpowered against a sub-0.1 % effect even at 40 replicates, but + the three uncle caps are independent measurements of the same underlying difference, so + pooling them buys back a factor of ~sqrt(3) and is what actually resolves the trend. + """ + u = g[g.max_uncles > 0] + rows = [] + for d, s in u.groupby(DELAY): + w = 1.0 / s.se.to_numpy() ** 2 + p = float((s.gap.to_numpy() * w).sum() / w.sum()) + e = float(np.sqrt(1.0 / w.sum())) + rows.append({DELAY: d, "gap": p, "se": e, "ci95": Z95 * e, + "t": abs(p) / e if e > 0 else np.inf}) + return pd.DataFrame(rows).sort_values(DELAY) + + +def fig_gap(g: pd.DataFrame) -> plt.Figure: + """The countable − unrestricted gap with 95% CIs, zoomed to the U >= 1 scale. + + The U=0 negative control is NOT plotted as a band here: with no uncles the models are + identical by construction, but the unrecovered regime is so noisy that its CI (±0.025) + is ~17x the entire range of the U >= 1 gaps and would fill the axes. Its magnitude is + annotated instead — the point being that the control's noise floor lives far outside + anything the uncle arms show, so those arms are measuring signal, not spread. + """ + fig, ax = plt.subplots(figsize=(6.6, 4.2)) + pooled = pooled_by_delay(g) + for i, u in enumerate(sorted(g["max_uncles"].unique())): + if u == 0: + continue + a = g[g.max_uncles == u].sort_values(DELAY) + ax.errorbar(a[DELAY], a.gap, yerr=a.ci95, fmt="-o", color=style.color_for(i), + label=f"U={u}", ms=4, capsize=3, lw=1.0, alpha=0.75) + ax.errorbar(pooled[DELAY], pooled.gap, yerr=pooled.ci95, fmt="-D", color="0.15", + label="pooled over U≥1", ms=5, capsize=4, lw=1.8, zorder=5) + ax.axhline(0.0, color="0.3", lw=0.9, ls=":") + ax.set_xlabel("max per-relay mixing delay (slots)") + ax.set_ylabel(r"$\hat{D}/D$ gap: countable $-$ unrestricted") + ax.set_title("The first-fork cost across the design band (95% CI)") + ctl = g[g.max_uncles == 0] + if len(ctl): + band = float(ctl.ci95.max()) + span = float(np.abs(np.r_[g[g.max_uncles > 0].gap + g[g.max_uncles > 0].ci95, + g[g.max_uncles > 0].gap - g[g.max_uncles > 0].ci95]).max()) + ax.set_ylim(-1.35 * span, 1.35 * span) + ax.text(0.015, 0.03, + f"U=0 negative control (true gap = 0): 95% CI ±{band:.4f}, " + f"{band / span:.0f}× outside this range", + transform=ax.transAxes, fontsize=6.5, alpha=0.75) + ax.legend(fontsize="x-small", ncol=2) + return fig + + +def main() -> None: + ap = argparse.ArgumentParser(description=__doc__.splitlines()[0]) + ap.add_argument("--countable", required=True, help="run dir of fine-countable") + ap.add_argument("--old", required=True, help="run dir of fine-old") + ap.add_argument("--out", default="figures/fine-delay") + args = ap.parse_args() + style.apply_style() + out = Path(args.out) + out.mkdir(parents=True, exist_ok=True) + + cnt, old = _cells(_load(args.countable)), _cells(_load(args.old)) + g = gaps(cnt, old) + prov = "tsi-sim-pernode fine-delay.yaml (+--old)" + + written = [] + written += style.save(fig_accuracy(cnt, old), out / "fine_accuracy_vs_delay", prov) + written += style.save(fig_gap(g), out / "fine_gap_vs_delay", prov) + + print(f"{'cell':<16} {'countable':>17} {'unrestricted':>17} " + f"{'gap':>9} {'95% CI':>9} {'t':>6} verdict") + for _, r in g.iterrows(): + verdict = ("CONTROL (true gap = 0)" if r.max_uncles == 0 else + "resolved" if r.t >= 2 else "no difference resolved") + print(f"U={int(r.max_uncles)} delay={r[DELAY]:>5g} " + f"{r.mean_ratio_c:.4f}+-{r.sem_ratio_c:.4f} " + f"{r.mean_ratio_o:.4f}+-{r.sem_ratio_o:.4f} " + f"{r.gap:+.4f} +-{r.ci95:.4f} {r.t:6.2f} {verdict}") + worst = g[g.max_uncles > 0] + print(f"\nn_rep = {int(g.n_rep_c.min())}/{int(g.n_rep_o.min())} per arm") + print(f"widest 95% CI half-width at U>=1: +-{worst.ci95.max():.4f} " + f"({100 * worst.ci95.max():.2f} pp)") + # Per-cell significance must be read against the number of cells tested: with 15 cells, + # ~0.75 are expected to clear t=2 by chance alone, so quote the Bonferroni threshold. + bonf = 2.935 if len(worst) == 15 else float("nan") + print(f"per-cell: {int((worst.t >= 2).sum())}/{len(worst)} cells with t>=2 " + f"(expected by chance {0.05 * len(worst):.2f}); max t = {worst.t.max():.2f} " + f"vs Bonferroni threshold {bonf:.3f}") + + print("\npooled over U>=1 (the three caps measure the same difference):") + pooled = pooled_by_delay(g) + for _, r in pooled.iterrows(): + mark = " <-- resolved" if r.t >= 2 else "" + print(f" delay={r[DELAY]:>4g}: {r.gap:+.5f} +-{r.ci95:.5f} t={r.t:5.2f}{mark}") + w = 1.0 / worst.se.to_numpy() ** 2 + allp = float((worst.gap.to_numpy() * w).sum() / w.sum()) + alle = float(np.sqrt(1.0 / w.sum())) + print(f" whole band: {allp:+.5f} +-{Z95 * alle:.5f} t={abs(allp) / alle:.2f}") + + ctl = g[g.max_uncles == 0] + if len(ctl): + print(f"\nU=0 negative control (true gap = 0): |gap| up to {ctl.gap.abs().max():.4f}, " + f"max t = {ctl.t.max():.2f}, 95% CI +-{ctl.ci95.max():.4f} " + f"-> control {'PASSES' if ctl.t.max() < 2 else 'FAILS'}") + print(f"wrote {len(written)} files -> {out}") + + +if __name__ == "__main__": + main() diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py index 80945c2..4bc5081 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/measure.py @@ -12,7 +12,13 @@ Counting models (``countable`` flag; CLI ``--old`` clears it): (cryptarchia-v1-protocol.md): the reference must be within the window (``0 < slot_B - slot_U <= w``), the uncle must not lie on the counting chain, and its **parent must lie on the counting chain** (only the first block of a fork counts). - References failing the parent rule are tallied as ``deep`` diagnostics. + References failing the parent rule are tallied as ``deep``. On a real run that tally is + always ZERO and is a defensive invariant, not a measured rate: countable *selection* + already refuses non-first-fork candidates, and for a chain block ``B`` the producer's + chain below ``B`` is the same ancestor path as the counting chain below ``B``, so the + two rules cannot disagree. A non-zero ``deep`` means selection and counting have drifted + (asserted end-to-end by test_countable_counting.py). Only hand-baked references — the + ones the unit tests construct — can make it fire. * **old** — every baked reference in the measurement window counts (fork depth ignored), reproducing the pre-redesign behaviour. @@ -51,9 +57,11 @@ class Measurement: q: np.ndarray # (N,) honest active-slot fraction q_eff: np.ndarray # (N,) uncle-recovered fraction orphan_rate: np.ndarray # (N,) - ref_total: np.ndarray # (N,) distinct referenced uncles examined in the window - ref_deep: np.ndarray # (N,) of those, rejected by the parent-on-chain (first-fork) rule; - # always 0 under the old model (no rule to reject on) + ref_total: np.ndarray # (N,) distinct referenced uncles examined (slot in [0,T); the + # per-reference window check is applied after this tally) + ref_deep: np.ndarray # (N,) of those, rejected by the parent-on-chain (first-fork) rule. + # ALWAYS 0 on a real run under either model — a selection/ + # counting drift alarm, not a rate (see the module docstring) agreement_window: float agreement_tip: float diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py index e7c3164..dfad269 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py @@ -27,6 +27,27 @@ CONFIG_COLS = ["n_nodes", "stake_dist", "pareto_shape", "topology", "degree", GRAPH_TOPOLOGIES = ("regular", "blend") +def sem(x) -> float: + """Standard error of the mean over replicates (0 for a single replicate). + + Replicate spread is the only uncertainty estimate these sweeps carry, and at high + mixing delay it is large enough to swamp the effects being compared — so any figure or + table quoting a cell mean should quote this alongside it. + """ + x = np.asarray(x, dtype=float) + return float(x.std(ddof=1) / np.sqrt(len(x))) if len(x) > 1 else 0.0 + + +def recovery_rate(q, q_u): + """Invert ``theory.q_effective``: ``r = (q_u - q) / (1 - q)``. + + The share of wasted active slots that a countable uncle reference puts back into the + count. Clamped denominator so a saturated ``q -> 1`` cell stays finite. + """ + q, q_u = np.asarray(q, dtype=float), np.asarray(q_u, dtype=float) + return (q_u - q) / np.maximum(1.0 - q, 1e-12) + + def _lat_axis(topo: str) -> tuple[str, str]: """(dataframe column, axis label) for the dominant latency knob of a graph topology.""" if topo == "blend": diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py index 04cc065..ba11961 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/uncles.py @@ -16,79 +16,21 @@ block id only (no slot exclusion). Selected refs are baked at production and immutable once adopted, so density counting stays view-independent under both models. + +``select_uncles_at_production`` is the ONLY selection entry point — blocktree.py calls it +once per produced block. Tests drive it through the same signature (see +tests/test_uncles.py ``annotate_via_production``) rather than through a parallel offline +implementation, so there is no second copy of the rules to drift out of sync. """ from __future__ import annotations import numpy as np -from .blocktree import GENESIS, BlockTree +from .blocktree import GENESIS from .config import SimConfig -def _orphans_sorted(tree: BlockTree, canonical_ids: list[int]) -> tuple[np.ndarray, np.ndarray]: - """Return orphan block ids sorted by (slot, id) and their slots.""" - canonical = np.zeros(tree.n_blocks, dtype=bool) - canonical[canonical_ids] = True - all_real = np.arange(1, tree.n_blocks) - orphan_ids = all_real[~canonical[1:]] - orphan_slots = tree.slot[orphan_ids] - order = np.lexsort((orphan_ids, orphan_slots)) # by slot, then id - return orphan_ids[order], orphan_slots[order] - - -def annotate_uncles( - tree: BlockTree, canonical_ids: list[int], config: SimConfig, rng: np.random.Generator -) -> None: - """Fill ``tree.uncles[B]`` for every canonical block ``B`` per the selection rule (offline). - - Countable model: candidates are restricted to orphans whose parent is canonical (first - fork blocks), slots already occupied on the chain are excluded, and at most one uncle - per slot is picked. Old model: any orphan in the window, dedup by id only. - """ - u_max = config.max_uncles - if u_max <= 0: - return - w = config.effective_uncle_window - orphan_ids, orphan_slots = _orphans_sorted(tree, canonical_ids) - if orphan_ids.size == 0: - return - - countable = config.uncle_model != "old" - occupied: set[int] = set() - if countable: - canonical = set(canonical_ids) - keep = [i for i in range(orphan_ids.size) - if int(tree.parent[orphan_ids[i]]) == GENESIS - or int(tree.parent[orphan_ids[i]]) in canonical] - orphan_ids, orphan_slots = orphan_ids[keep], orphan_slots[keep] - if orphan_ids.size == 0: - return - occupied = {int(tree.slot[b]) for b in canonical_ids} - - referenced: set[int] = set() - # oldest canonical block first - for b in reversed(canonical_ids): - sb = int(tree.slot[b]) - lo = int(np.searchsorted(orphan_slots, sb - w, side="left")) # slot_U >= sb - w - hi = int(np.searchsorted(orphan_slots, sb, side="left")) # slot_U < sb - if hi <= lo: - continue - window_ids = orphan_ids[lo:hi] # already oldest-first - if countable: - window_ids = np.array( - [x for x in window_ids.tolist() if int(tree.slot[x]) not in occupied], - dtype=np.int64, - ) - selected = _select(window_ids, referenced, config, rng, - slot=tree.slot, one_per_slot=countable) - if selected: - tree.uncles[b] = tuple(selected) - referenced.update(selected) - if countable: - occupied.update(int(tree.slot[u]) for u in selected) - - def _select( window_ids: np.ndarray, referenced: set[int], diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py index 748516a..b23a573 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_countable_counting.py @@ -82,3 +82,28 @@ def test_window_recheck_rejects_stale_reference(): tree = _tree() assert countable_refs(tree, CANONICAL, 2) == {5} # 7, 8 now out of window (d=3) assert density_m(tree, CANONICAL, T, countable=True, w=2) == 5 + + +def test_deep_ref_share_is_zero_end_to_end(): + """The counting-side parent-on-chain re-check must never fire on a real countable run. + + Countable SELECTION already refuses to reference a non-first-fork block, and for a + block ``b`` on the counting chain the producer's chain below ``b`` IS the counting + chain below ``b`` (they are the same ancestor path). So ``ref_deep`` is a defensive + invariant, not a measured rate: any non-zero value means selection and counting have + drifted apart. The hand-built trees above are the only way to make it fire — they bake + references selection would never emit. + """ + import pandas as pd + + from tsi_sim.config import SimConfig + from tsi_sim.engine import run_trajectory + + # Small but fork-rich: Blend delay spreads proposals over many slots. + cfg = SimConfig(n_nodes=60, topology="blend", blend_hops=2, blend_delay_max=8.0, + degree=4, max_uncles=2, k=32, epochs=3, f=0.1, + stake_dist="pareto", init_dest="common") + df = pd.DataFrame(run_trajectory(cfg)) + assert df.n_blocks.sum() > 0 # the run actually produced blocks + assert (df.deep_ref_share == 0.0).all(), ( + f"counting rejected references selection emitted: {df.deep_ref_share.tolist()}") diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_theory.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_theory.py index 8141e8b..b0f6f98 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_theory.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_theory.py @@ -38,3 +38,46 @@ def test_fixed_point_bias_about_one_percent(): b = theory.fixed_point_bias(F) assert abs(b - (F / (33 / 1000))) < 1e-12 assert 1.005 < b < 1.02 + + +def test_q_effective_interpolates_between_q_and_one(): + # r = 0 -> no recovery (chain-only q); r = 1 -> every wasted slot recovered (q_u = 1). + for q in (0.3, 0.65, 0.9): + assert abs(float(theory.q_effective(q, 0.0)) - q) < 1e-15 + assert abs(float(theory.q_effective(q, 1.0)) - 1.0) < 1e-15 + # monotone and strictly between for partial recovery + half = float(theory.q_effective(q, 0.5)) + assert q < half < 1.0 + + +def test_q_effective_round_trips_the_measured_recovery_rate(): + # The identity the report quotes: given measured q and q_u, r = (q_u - q)/(1 - q) + # reconstructs q_u exactly. This is how plot_countable_vs_old.py derives its overlay. + for q, q_u in ((0.3129, 0.6147), (0.5380, 0.9874), (0.7485, 0.9992)): + r = (q_u - q) / (1.0 - q) + assert abs(float(theory.q_effective(q, r)) - q_u) < 1e-12 + + +def test_q_effective_recovers_unbiased_equilibrium(): + # Full recovery must lift the equilibrium to exactly 1 for any starting q. + for q in (0.3, 0.65, 0.9): + assert abs(float(theory.expected_ratio(F, theory.q_effective(q, 1.0))) - 1.0) < 1e-12 + + +def test_window_miss_prob_decays_as_exp_minus_w(): + # P(no canonical block in w_u = W/f slots) = (1-f)^(W/f) = exp(W * ln(1-f)/f). + # The docstring's "~ e^-W" is the f -> 0 limit: ln(1-f)/f = -(1 + f/2 + ...) = -1.0170 + # at f = 1/30, so the true decay is slightly FASTER than e^-W, by a factor that grows + # with W (16% low by W = 10). Assert the exact form, and bracket the heuristic. + rate = np.log(1.0 - F) / F + assert -1.02 < rate < -1.0 + for w_abs in (1.0, 3.0, 10.0): + p = float(theory.window_miss_prob(F, w_abs)) + assert abs(p - (1.0 - F) ** (w_abs / F)) < 1e-15 + assert abs(p - np.exp(rate * w_abs)) < 1e-15 # exact closed form + assert np.exp(-1.02 * w_abs) < p < np.exp(-w_abs) # brackets the e^-W heuristic + # the spec default W = 10 makes the window a negligible loss channel + assert float(theory.window_miss_prob(F, 10.0)) < 1e-4 + # strictly decreasing in W + ps = [float(theory.window_miss_prob(F, w)) for w in (1, 2, 3, 5, 7, 10)] + assert all(a > b for a, b in zip(ps[:-1], ps[1:], strict=True)) diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py index 4240cc8..8807728 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_uncles.py @@ -2,7 +2,7 @@ import numpy as np from tsi_sim.blocktree import BlockTree from tsi_sim.config import SimConfig -from tsi_sim.uncles import annotate_uncles +from tsi_sim.uncles import select_uncles_at_production def make_tree(slots, parents, heights, leaders): @@ -16,6 +16,23 @@ def make_tree(slots, parents, heights, leaders): ) +def annotate_via_production(tree, canonical_ids, config, rng): + """Fill ``tree.uncles`` by replaying the PRODUCTION selection for each canonical block. + + The simulator has exactly one selection implementation + (``select_uncles_at_production``, called from blocktree.py per produced block); this + replays it offline — oldest canonical block first, each block selecting as its producer + would have at ``t = slot[b]`` extending ``parent[b]`` — so the tests below exercise the + live code path rather than a parallel offline copy. Requires ``tree.slot`` ascending by + block id (true for every tree these tests build, and for real runs). + """ + arrival = np.zeros(tree.n_blocks) # every block already in the producer's view + for b in reversed(canonical_ids): # oldest first, so earlier refs are visible + tree.uncles[b] = select_uncles_at_production( + tree.slot, tree.parent, tree.uncles, arrival, nb=tree.n_blocks, + parent_id=int(tree.parent[b]), t=int(tree.slot[b]), config=config, rng=rng) + + def _canonical_and_orphan_tree(): # genesis(0); canonical chain 1(slot0)->3(slot3)->4(slot5); orphan 2(slot1) tree = make_tree( @@ -31,7 +48,7 @@ def _canonical_and_orphan_tree(): def test_oldest_selection_and_window(): tree, canonical = _canonical_and_orphan_tree() cfg = SimConfig(max_uncles=1, uncle_window=300, uncle_strategy="oldest") - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) # orphan 2 (slot1) is within window of block 3 (slot3) -> referenced there referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == {2} @@ -40,7 +57,7 @@ def test_oldest_selection_and_window(): def test_no_uncles_when_u_zero(): tree, canonical = _canonical_and_orphan_tree() cfg = SimConfig(max_uncles=0) - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) assert all(tree.uncles[b] == () for b in canonical) @@ -49,7 +66,7 @@ def test_window_excludes_out_of_range_orphan(): # and derives the window from window_absorption — see the countable twin below.) tree, canonical = _canonical_and_orphan_tree() cfg = SimConfig(max_uncles=1, uncle_window=1, uncle_strategy="oldest", uncle_model="old") - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) # orphan 2 at slot1; nearest canonical after it is block3 at slot3 -> gap 2 > W=1 referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == set() @@ -61,14 +78,14 @@ def test_countable_window_is_derived_from_absorption(): tree, canonical = _canonical_and_orphan_tree() cfg = SimConfig(max_uncles=1, f=0.5, window_absorption=1.0) assert cfg.effective_uncle_window == 2 - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == {2} # block3 (slot3) still reaches it # shrink f so the derived window rounds to 1 slot: gap 2 > 1 -> excluded tree2, canonical2 = _canonical_and_orphan_tree() cfg2 = SimConfig(max_uncles=1, f=0.9, window_absorption=1.0) assert cfg2.effective_uncle_window == 1 - annotate_uncles(tree2, canonical2, cfg2, np.random.default_rng(0)) + annotate_via_production(tree2, canonical2, cfg2, np.random.default_rng(0)) assert {u for b in canonical2 for u in tree2.uncles[b]} == set() @@ -88,8 +105,8 @@ def test_random_strategy_deterministic_and_capped(): tree_a, canon = _wide_orphan_tree() tree_b, _ = _wide_orphan_tree() cfg = SimConfig(max_uncles=2, uncle_window=300, uncle_strategy="random", uncle_random_p=0.5) - annotate_uncles(tree_a, canon, cfg, np.random.default_rng(7)) - annotate_uncles(tree_b, canon, cfg, np.random.default_rng(7)) + annotate_via_production(tree_a, canon, cfg, np.random.default_rng(7)) + annotate_via_production(tree_b, canon, cfg, np.random.default_rng(7)) assert tree_a.uncles == tree_b.uncles # same seed -> identical total = sum(len(tree_a.uncles[b]) for b in canon) assert total <= cfg.max_uncles # capped @@ -99,18 +116,20 @@ def test_random_p_one_matches_oldest(): import numpy as np tree_r, canon = _wide_orphan_tree() tree_o, _ = _wide_orphan_tree() - annotate_uncles(tree_r, canon, SimConfig(max_uncles=2, uncle_strategy="random", - uncle_random_p=1.0), np.random.default_rng(1)) - annotate_uncles(tree_o, canon, SimConfig(max_uncles=2, uncle_strategy="oldest"), - np.random.default_rng(1)) + annotate_via_production(tree_r, canon, SimConfig(max_uncles=2, uncle_strategy="random", + uncle_random_p=1.0), + np.random.default_rng(1)) + annotate_via_production(tree_o, canon, SimConfig(max_uncles=2, uncle_strategy="oldest"), + np.random.default_rng(1)) assert tree_r.uncles == tree_o.uncles # p=1 deterministically takes oldest-first def test_random_p_zero_selects_nothing(): import numpy as np tree, canon = _wide_orphan_tree() - annotate_uncles(tree, canon, SimConfig(max_uncles=4, uncle_strategy="random", - uncle_random_p=0.0), np.random.default_rng(1)) + annotate_via_production(tree, canon, SimConfig(max_uncles=4, uncle_strategy="random", + uncle_random_p=0.0), + np.random.default_rng(1)) assert all(tree.uncles[b] == () for b in canon) @@ -124,7 +143,7 @@ def test_dedup_across_ancestors(): ) canonical = [4, 3, 1] cfg = SimConfig(max_uncles=4, uncle_window=300, uncle_strategy="oldest") - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) counts = sum(len(tree.uncles[b]) for b in canonical) assert counts == 1 # orphan 2 referenced exactly once despite two eligible blocks @@ -147,7 +166,7 @@ def _deep_fork_tree(): def test_countable_excludes_deep_fork_blocks(): tree, canonical = _deep_fork_tree() cfg = SimConfig(max_uncles=4) - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == {2, 4} # deep block 3 (parent is an orphan) excluded @@ -155,7 +174,7 @@ def test_countable_excludes_deep_fork_blocks(): def test_old_model_still_references_deep_fork_blocks(): tree, canonical = _deep_fork_tree() cfg = SimConfig(max_uncles=4, uncle_model="old", uncle_window=300) - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) referenced = {u for b in canonical for u in tree.uncles[b]} assert referenced == {2, 3, 4} # --old: fork depth ignored @@ -170,7 +189,7 @@ def test_countable_excludes_occupied_slots_and_dedups_per_slot(): ) canonical = [5, 1] cfg = SimConfig(max_uncles=4) - annotate_uncles(tree, canonical, cfg, np.random.default_rng(0)) + annotate_via_production(tree, canonical, cfg, np.random.default_rng(0)) referenced = {u for b in canonical for u in tree.uncles[b]} # slot0 is canonical-occupied -> orphan 2 excluded; slot2 pair -> exactly one picked assert referenced == {3} @@ -196,3 +215,53 @@ def test_production_selection_countable_rules(): slot, parent, uncles, arrival, nb=6, parent_id=1, t=5, config=old, rng=np.random.default_rng(0)) assert sel_old == (2, 3, 4, 5) # --old: depth and slot-dedup ignored + + +def test_production_parent_below_window_resolves_chain_membership(): + """Candidate parents can sit BELOW the reference window (uncles.py `pmin`/`below` walk). + + The window walk only establishes chain membership for ancestors with slot >= t-w, so a + candidate whose parent is older than that needs the extra walk down to `pmin`. With a + narrow window this is the branch that decides first-fork eligibility. + + chain 1(s0) -> 2(s1) -> 6(s8); off-chain 7(s2, parent 3) where 3(s2) is NOT on the chain. + Candidates at t=9 with w=4 are the blocks in slots [5,9): 4(s5, parent 2 -> ON chain, + countable) and 5(s6, parent 3 -> OFF chain, deep). Both parents sit below the window, + so only the `below` walk can tell them apart. + """ + from tsi_sim.uncles import select_uncles_at_production + + # id: 0 1 2 3 4 5 6 + slot = np.array([-1, 0, 1, 2, 5, 6, 8], np.int64) + parent = np.array([-1, 0, 1, 1, 2, 3, 2], np.int64) + uncles: list = [() for _ in range(7)] + arrival = np.zeros(7) + # w = round(1/0.25) = 4 slots; window at t=9 is [5, 9) + cfg = SimConfig(max_uncles=4, f=0.25, window_absorption=1.0) + assert cfg.effective_uncle_window == 4 + sel = select_uncles_at_production( + slot, parent, uncles, arrival, nb=7, parent_id=6, t=9, config=cfg, + rng=np.random.default_rng(0)) + assert sel == (4,) # 5 rejected: parent 3 is off-chain (deep) and below the window + + +def test_production_excludes_slots_occupied_by_chain_and_prior_uncles(): + """The occupied-slot exclusion is built from the producer's chain walk (uncles.py). + + chain 1(s0) -> 2(s1) -> 5(s4); block 2 already references uncle 3(s2). Candidates at + t=5 are 3 (already referenced), 4(s2, same slot as the referenced 3 -> slot occupied) + and 6(s3, free slot). Only 6 survives. + """ + from tsi_sim.uncles import select_uncles_at_production + + # id: 0 1 2 3 4 5 6 + slot = np.array([-1, 0, 1, 2, 2, 4, 3], np.int64) + parent = np.array([-1, 0, 1, 1, 1, 2, 1], np.int64) + uncles: list = [() for _ in range(7)] + uncles[2] = (3,) # block 2 already referenced uncle 3 + arrival = np.zeros(7) + cfg = SimConfig(max_uncles=4) # w = 300, whole tree in window + sel = select_uncles_at_production( + slot, parent, uncles, arrival, nb=7, parent_id=5, t=5, config=cfg, + rng=np.random.default_rng(0)) + assert sel == (6,) # 3 already referenced; 4 shares slot 2 with it; 6 is free From 15e876e90a3ffc0aaa4d22a96bd5c1d3928b4d5e Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Wed, 5 Aug 2026 10:34:33 +0200 Subject: [PATCH 04/22] Correctness pass: derive rho in code, and the absolute vs-1.0 test Two findings from re-reviewing the fine-delay section. 1. The rho values I put in s3.2a were wrong. The report derives rho = f*D_vis with D_vis = hops*delta_max/2 + (hops+1)*ell_mean from a MEASURED ell_mean (1.211 slots at N=1000/degree=6), not from the link_latency_mean parameter (0.5). Hand-substituting a guessed 1.5 inflated every value by ~0.04: the band is rho 0.21-0.41, not 0.25-0.45. To stop that recurring, graph_ell_mean moves out of rho_boundary_analysis.py into figures_pernode.py, joined by a new rho_for() that both scripts and any future quotation go through; plot_fine_delay.py now prints the derived rho per delay. This also exposed an inconsistency in the existing s3.2 table, which rounded delta_max=4 to "rho ~ 0.4" while s3.2a called the same cell 0.36 and prose elsewhere already used 0.56 for delta_max=8. The s3.2 column now carries the derived values (0.36/0.56/0.96/1.76). 2. Testing each cell against the exact target 1.0 -- the same question the gap test asks, without reference to the other model -- corroborates the first-fork onset independently. Unrestricted: 1/15 cells below 1 (t=-2.09, chance). Countable: 4/15, and not scattered -- delta_max=4 at U=1, and ALL THREE caps at delta_max=5 (-0.0012 to -0.0019, t=-2.5..-3.7). A shortfall appearing at every cap at once, only at the top of the band, only under the restricted model, is the first-fork cost seen absolutely. That makes "one uncle slot is sufficient -- not approximately, exactly" too strong as I had written it. s3.2a now states the residual (0.1-0.2% at the top of the band, zero below delta_max=3), reconciles it with the s1 headline, and notes that since all three caps show the same shortfall the residual is not a capacity limit. The bound quoted in s1 moves from "below 0.15%" to "<= 0.2%". Also adds the new run directories to s9's canonical list, which covered every other study but not these. Tests: 209 passed. ruff clean. Co-Authored-By: Claude Opus 5 (1M context) --- ...i-report-1-overview-and-recommendations.md | 2 +- .../tsi/tsi-report-2-accuracy-and-design.md | 32 ++++++++-------- ...report-4-reproducibility-and-appendices.md | 4 +- .../scripts/plot_fine_delay.py | 38 ++++++++++++++++++- .../scripts/rho_boundary_analysis.py | 21 +--------- .../src/tsi_sim/plotting/figures_pernode.py | 35 +++++++++++++++++ 6 files changed, 92 insertions(+), 40 deletions(-) diff --git a/reports/tsi/tsi-report-1-overview-and-recommendations.md b/reports/tsi/tsi-report-1-overview-and-recommendations.md index 4491dfb..c5df0eb 100644 --- a/reports/tsi/tsi-report-1-overview-and-recommendations.md +++ b/reports/tsi/tsi-report-1-overview-and-recommendations.md @@ -8,7 +8,7 @@ --- -> **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](tsi-report-2-accuracy-and-design.md#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2), [§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.25–0.45`) puts every `U ≥ 1` cell of both models in 0.998–1.001, resolves no difference in any individual cell (widest 95 % CI ±0.15 pp), and bounds the pooled first-fork cost below **0.15 %** — rising monotonically with delay and separating from zero only at the top of the band ([§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. +> **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](tsi-report-3-robustness-and-incentives.md#s6-7)–[§6.8](tsi-report-3-robustness-and-incentives.md#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](tsi-report-2-accuracy-and-design.md#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2), [§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.21–0.41`) puts every `U ≥ 1` cell of both models in 0.998–1.001, resolves no difference in any individual cell (widest 95 % CI ±0.15 pp), and bounds the first-fork cost at **≤ 0.2 %** — indistinguishable from zero through `δ_max` ≤ 3 and rising monotonically with delay thereafter ([§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. ## 1. Executive summary diff --git a/reports/tsi/tsi-report-2-accuracy-and-design.md b/reports/tsi/tsi-report-2-accuracy-and-design.md index 577038e..00d9f2b 100644 --- a/reports/tsi/tsi-report-2-accuracy-and-design.md +++ b/reports/tsi/tsi-report-2-accuracy-and-design.md @@ -116,12 +116,12 @@ The U = 0 under-count **deepens with N** (more nodes → more concurrent proposa | `δ_max` (s) | ρ | U | countable | unrestricted | gap (t) | |---|---|---|---|---|---| -| 4 | ≈ 0.4 | 1 / 2 / 4 | 0.9979 ± 0.0015 / 0.9982 ± 0.0014 / 0.9995 ± 0.0012 | 0.9981 ± 0.0006 / 0.9985 ± 0.0012 / 0.9992 ± 0.0013 | *none resolved* (0.1–0.2) | -| 8 | ≈ 0.6 | 1 / 2 / 4 | 0.9965 ± 0.0015 / 0.9955 ± 0.0017 / 0.9963 ± 0.0015 | 0.9986 ± 0.0017 / 0.9993 ± 0.0016 / 0.9989 ± 0.0017 | *none resolved* (1.0–1.6) | -| 16 | ≈ 1.0 | 1 | 0.9647 ± 0.0065 | 0.9610 ± 0.0043 | *not resolved* (0.5) | -| 16 | ≈ 1.0 | 2 / 4 | 0.9862 ± 0.0010 / 0.9911 ± 0.0032 | 0.9999 ± 0.0005 / 1.0013 ± 0.0011 | −0.014 (12.1) / −0.010 (3.0) | -| 32 | ≈ 1.8 | 1 | 0.608 ± 0.069 | 0.570 ± 0.042 | *not resolved* (0.5) | -| 32 | ≈ 1.8 | 2 / 4 | 0.9343 ± 0.0015 / 0.9517 ± 0.0007 | 0.9774 ± 0.0064 / 1.0020 ± 0.0010 | −0.043 (6.5) / −0.050 (41.0) | +| 4 | ≈ 0.36 | 1 / 2 / 4 | 0.9979 ± 0.0015 / 0.9982 ± 0.0014 / 0.9995 ± 0.0012 | 0.9981 ± 0.0006 / 0.9985 ± 0.0012 / 0.9992 ± 0.0013 | *none resolved* (0.1–0.2) | +| 8 | ≈ 0.56 | 1 / 2 / 4 | 0.9965 ± 0.0015 / 0.9955 ± 0.0017 / 0.9963 ± 0.0015 | 0.9986 ± 0.0017 / 0.9993 ± 0.0016 / 0.9989 ± 0.0017 | *none resolved* (1.0–1.6) | +| 16 | ≈ 0.96 | 1 | 0.9647 ± 0.0065 | 0.9610 ± 0.0043 | *not resolved* (0.5) | +| 16 | ≈ 0.96 | 2 / 4 | 0.9862 ± 0.0010 / 0.9911 ± 0.0032 | 0.9999 ± 0.0005 / 1.0013 ± 0.0011 | −0.014 (12.1) / −0.010 (3.0) | +| 32 | ≈ 1.76 | 1 | 0.608 ± 0.069 | 0.570 ± 0.042 | *not resolved* (0.5) | +| 32 | ≈ 1.76 | 2 / 4 | 0.9343 ± 0.0015 / 0.9517 ± 0.0007 | 0.9774 ± 0.0064 / 1.0020 ± 0.0010 | −0.043 (6.5) / −0.050 (41.0) | **The `U = 0` rows are a negative control.** With no uncles the two models are identical by construction — no reference is ever taken, so any measured gap is pure between-run noise (the two models draw independent RNG streams by design, so the comparison is unpaired). That control reads **+0.010 (t = 0.8) at `δ_max = 4`** but **−0.230 (t = 2.1) at `δ_max = 32`**, where single replicates range from 0.05 to 0.60. Read the table against that floor: at `δ_max = 32` a gap must clear ~0.2 to mean anything on a single-replicate basis, which is exactly why the `U = 1` cells there are reported as unresolved while the tightly-clustered `U = 2` and `U = 4` cells are not. @@ -144,29 +144,31 @@ So: **at the operating loads (`ρ < 1`) no difference between the models is dete **The question.** [§3.2](#s3-2) samples the mixing delay at 4/8/16/32. That resolves the overload regime, but it leaves the band the parameters are actually chosen in — the low-delay end, where every operating point sits — measured at four-fold spacing and five replicates, which is enough to say "no difference detected" and nothing more. How accurate is TSI across `δ_max` = 1–5, and how large a first-fork cost can be *excluded* there? -**The finding.** With one uncle slot the estimate is exact across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay. Without uncles the same band decays steeply, 0.810 → 0.640. Through `δ_max ≤ 4` the two referencing models are **indistinguishable**, and the first-fork restriction begins to cost something measurable only at the top of the band. +**The finding.** One uncle slot holds the estimate at the true stake across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay, while the uncle-free baseline decays 0.810 → 0.640. The two referencing models are **indistinguishable through `δ_max` ≤ 3**; at the top of the band the first-fork restriction becomes measurable and costs **0.1–0.2 %**. Two independent tests — the model-vs-model gap, and each model against the exact target 1.0 — agree on that onset. -`configs/fine-delay.yaml` spends replicates instead of range — `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, **40 replicates** per cell (8× [§3.2](#s3-2)), N = 1 000, blend, 3 hops — run under both models ([§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The band spans `ρ ≈ 0.25` to `0.45`, entirely inside the design regime. +`configs/fine-delay.yaml` spends replicates instead of range — `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, **40 replicates** per cell (8× [§3.2](#s3-2)), N = 1 000, blend, 3 hops — run under both models ([§9](tsi-report-4-reproducibility-and-appendices.md#s9)). The band spans `ρ ≈ 0.21` to `0.41`, entirely inside the design regime. | `δ_max` (s) | ρ | `U=0` countable / unrestricted | `U≥1` countable | `U≥1` unrestricted | pooled gap (t) | |---|---|---|---|---|---| -| 1 | ≈ 0.25 | 0.810 / 0.806 | 0.9994 – 0.9999 | 0.9990 – 1.0010 | −0.0004 ± 0.0007 (1.1) | -| 2 | ≈ 0.30 | 0.762 / 0.763 | 0.9996 – 1.0002 | 0.9996 – 1.0003 | +0.0000 ± 0.0008 (0.0) | -| 3 | ≈ 0.35 | 0.716 / 0.723 | 0.9995 – 1.0002 | 0.9992 – 1.0004 | −0.0001 ± 0.0008 (0.2) | -| 4 | ≈ 0.40 | 0.664 / 0.668 | 0.9988 – 0.9996 | 0.9995 – 0.9999 | −0.0005 ± 0.0008 (1.3) | -| 5 | ≈ 0.45 | 0.640 / 0.623 | 0.9982 – 0.9988 | 0.9995 – 1.0003 | **−0.0014 ± 0.0007 (3.7)** | +| 1 | ≈ 0.21 | 0.810 / 0.806 | 0.9994 – 0.9999 | 0.9990 – 1.0010 | −0.0004 ± 0.0007 (1.1) | +| 2 | ≈ 0.26 | 0.762 / 0.763 | 0.9996 – 1.0002 | 0.9996 – 1.0003 | +0.0000 ± 0.0008 (0.0) | +| 3 | ≈ 0.31 | 0.716 / 0.723 | 0.9995 – 1.0002 | 0.9992 – 1.0004 | −0.0001 ± 0.0008 (0.2) | +| 4 | ≈ 0.36 | 0.664 / 0.668 | 0.9988 – 0.9996 | 0.9995 – 0.9999 | −0.0005 ± 0.0008 (1.3) | +| 5 | ≈ 0.41 | 0.640 / 0.623 | 0.9982 – 0.9988 | 0.9995 – 1.0003 | **−0.0014 ± 0.0007 (3.7)** | **No individual cell resolves a model difference.** Across the 15 `U ≥ 1` cells the widest 95 % CI half-width is ±0.0015, one cell clears `t = 2` (0.75 are expected to by chance), and its `t = 2.59` does not survive the Bonferroni threshold of 2.94 for 15 tests. Read cell by cell, the honest statement is that any difference is **smaller than ±0.15 pp**. **Pooled, a small delay-dependent cost appears.** The three uncle caps are independent measurements of the same underlying difference, so inverse-variance pooling across them buys ~√3 in precision. Pooled per delay, `δ_max` 1–4 stay unresolved (|t| ≤ 1.3) while **`δ_max = 5` resolves at −0.0014 ± 0.0007 (t = 3.7)** — surviving correction for the five delays tested. Over the whole band the pooled gap is −0.00048 ± 0.00033 (t = 2.8), and 11 of 15 cells are negative. So the first-fork restriction does cost something, in the direction theory predicts, and the cost is **monotone in delay and below 0.15 % everywhere in this band** — negligible against the ±0.9 % per-epoch sampling noise of [Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB). (The pooling was chosen after inspecting the per-cell results; the per-delay trend, not the whole-band figure, is the defensible claim.) +**The absolute test agrees.** Asking the same question without reference to the other model — is each cell's equilibrium exactly 1.0? — reproduces the onset independently. Under the **unrestricted** model 1 of 15 cells sits significantly below 1 (`t` = −2.09, consistent with chance). Under the **countable** model 4 of 15 do, and they are not scattered: `δ_max = 4` at `U = 1` (−0.0012, `t` = −2.6) and **all three uncle caps at `δ_max = 5`** (−0.0012 to −0.0019, `t` = −2.5 to −3.7). A shortfall that appears at every cap simultaneously, only at the top of the band, and only under the restricted model, is the first-fork cost — the same effect the gap test resolves at `δ_max = 5`, seen from the absolute side. + **The negative control passes.** The `U = 0` arms — identical models by construction — show |gap| ≤ 0.016 with max `t` = 1.26, i.e. no spurious signal, but a 95 % CI of ±0.025: **17× wider than the entire `U ≥ 1` range.** The unrecovered regime is intrinsically noisy, which is precisely why the model comparison has to be made where uncles are active. -![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM over 40 replicates: every U ≥ 1 curve is pinned at 1.000 across the band under both models, while U = 0 (the negative control) decays 0.81 → 0.64.](report-figures/fig34_fine_delay_accuracy.png) +![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM over 40 replicates: every U ≥ 1 curve sits at 1.000 across the band under both models (to within 0.2 %), while U = 0 — the negative control — decays 0.81 → 0.64.](report-figures/fig34_fine_delay_accuracy.png) ![Fig 35 — the countable − unrestricted gap with 95% CIs, zoomed to the U ≥ 1 scale, with the inverse-variance pooled estimate in black: no single cell resolves, the pooled trend is monotone in delay, and only δ_max = 5 separates from zero (−0.0014 ± 0.0007).](report-figures/fig35_fine_delay_gap.png) -**What this settles.** One uncle slot is sufficient — not approximately, exactly — everywhere in the operating band, under either referencing model; the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.45`. And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **less than 0.15 %** anywhere a deployment should be operating. +**What this settles.** One uncle slot is sufficient everywhere in the operating band under either referencing model — the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.41`, and raising `U` past 1 buys nothing here (at `δ_max = 5` all three caps sit at the same 0.1–0.2 % shortfall, so the residual is *not* a capacity limit). And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **at most 0.2 %** anywhere a deployment should be operating — an order of magnitude below the ±0.9 % per-epoch sampling noise of [Appendix B](tsi-report-4-reproducibility-and-appendices.md#sB), and below the ~1 % fixed-point rounding bias of [Appendix A](tsi-report-4-reproducibility-and-appendices.md#sA). The [§1](tsi-report-1-overview-and-recommendations.md#s1) statement that one uncle restores the estimate to the true stake holds at the precision that matters; this section puts the residual at 0.1–0.2 % at the top of the band rather than zero. ### 3.3 One uncle is not always enough — the load `ρ` diff --git a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md index 473701b..61dc7d6 100644 --- a/reports/tsi/tsi-report-4-reproducibility-and-appendices.md +++ b/reports/tsi/tsi-report-4-reproducibility-and-appendices.md @@ -46,14 +46,14 @@ Sweep studies are committed configs, run with `make ` (writes a dated `run | U = 0 fluctuation series (zero delay, k ∈ {256, 1024, 2160}) | `scripts/appendix_fluct.py --run` (`runs/fluctuation_u0.parquet`) | [Appendix B](#sB) | | CI smoke grid + analytic sanity checks | `configs/smoke.yaml`; `scripts/verify.py` (`make verify`) — validation only, no figures | — | | **countable vs unrestricted referencing** (accuracy over delay × U; measured `q_u`/recovery `r`) | `configs/countable-vs-old.yaml` run twice — default and with `--old`; figures + significance table by `scripts/plot_countable_vs_old.py` | [§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) | -| **fine delay band** (δ_max 1–5 at 40 replicates; tight CI on the model gap in the design regime) | `configs/fine-delay.yaml` run twice — default and with `--old`; figure + table by `scripts/plot_fine_delay.py` | [§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a) | +| **fine delay band** (δ_max 1–5 at 40 replicates; tight CI on the model gap in the design regime) | `configs/fine-delay.yaml` run twice — default and with `--old`; figures + significance tables (model gap, and each model vs the exact 1.0 target) by `scripts/plot_fine_delay.py` | [§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a) | | **window absorption sweep** (`W` in expected block-intervals, `w_u = W/f` derived) | `configs/absorption-window.yaml`; figure by `scripts/plot_countable_vs_old.py` | [§3.4](tsi-report-2-accuracy-and-design.md#s3-4) | **Uncle-model convention.** The simulator's default is the **countable** model — first-fork candidates only, derived window `w_u = W/f`, occupied-slot exclusion, per-reference counting rules ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)). The **unrestricted** baseline is preserved in the code and selected with `--old` on `tsi-sweep`/`tsi-verify`. Its RNG key is byte-identical to the pre-restriction key, so `--old` **bit-reproduces the earlier runs**: a `rho-boundary` cell (δ_max = 8, U = 2, k = 256, N = 1 000) re-run under `--old` matches the committed `2026-07-27_195627_rho-boundary` parquet with `max |Δ| = 0` on every epoch and every metric. Studies in the table above that predate the countable default were produced under the unrestricted model and reproduce exactly under `--old`; the comparison rows quantify where the two models differ, and in the design regime (`ρ < 1`) no difference is resolvable, so those findings carry over unchanged. Because the two models draw independent RNG streams, every countable-vs-unrestricted comparison is **unpaired**, and its resolution is set by the replicate spread rather than by the effect size. Each comparison sweep therefore includes a `U = 0` arm as a **negative control**: with no uncles the models are identical by construction, so the measured `U = 0` gap is a direct reading of the noise floor at that delay and replicate count. At `δ_max = 32` with 5 replicates that floor is ≈ 0.23 in `D̂/D` — larger than several real effects elsewhere in the grid — which is why [§3.2](tsi-report-2-accuracy-and-design.md#s3-2) reports a `t` statistic per cell and why the design regime is measured separately at 40 replicates ([§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a)). -All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. +All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. Referencing-model studies: countable-vs-unrestricted = `2026-08-04_103536_cvo-countable` / `2026-08-04_104010_cvo-old`; window absorption = `2026-08-04_104633_absorption-window`; fine delay band = `2026-08-04_191441_fine-countable` / `2026-08-04_195353_fine-old`. Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` (block-rate `U_min` grid + ρ-collapse) rendered ad hoc from `runs/2026-07-24_043943_block-rate` with no committed generator; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` pool both sizes in that run, N = 5 000 and N = 10 000 — the generators filter on stake_dist/topology/degree/init_dest only, never on `n_nodes`); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay; `fig30`–`fig33` (countable-vs-unrestricted accuracy, `q_u`-prediction check, recovery rate, absorption-window sweep) by `scripts/plot_countable_vs_old.py` from the `cvo-countable`/`cvo-old`/`absorption-window` runs; `fig34`–`fig35` (design-regime accuracy and the model gap with 95 % CIs) by `scripts/plot_fine_delay.py` from the `fine-countable`/`fine-old` runs. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py index 5bfd32c..a2a10e9 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py @@ -34,7 +34,7 @@ import numpy as np import pandas as pd from tsi_sim.plotting import style -from tsi_sim.plotting.figures_pernode import equilibrium, sem +from tsi_sim.plotting.figures_pernode import equilibrium, rho_for, sem DELAY = "blend_delay_max" # Normal approximation: with 40 replicates per arm the t-quantile is within ~2% of 1.96, @@ -56,6 +56,20 @@ def _cells(df: pd.DataFrame) -> pd.DataFrame: mean_q_eff=("mean_q_eff", "mean")) +def vs_one(cells: pd.DataFrame) -> pd.DataFrame: + """Test each U >= 1 cell against the exact target 1.0. + + An independent read on the same question the gap test asks: the report's claim is that + uncle recovery restores the equilibrium to EXACTLY the true stake, so a systematic + shortfall across uncle caps is the first-fork cost seen from the absolute side rather + than differentially. 40 replicates give ~0.0005 resolution, enough to see 0.1%. + """ + u = cells[cells.max_uncles > 0].copy() + u["dev"] = u.mean_ratio - 1.0 + u["t"] = u.dev / u.sem_ratio.replace(0, np.nan) + return u.sort_values(["max_uncles", DELAY]) + + def gaps(cnt: pd.DataFrame, old: pd.DataFrame) -> pd.DataFrame: """countable - unrestricted per cell, with the unpaired SE and 95% CI half-width.""" m = cnt.merge(old, on=[DELAY, "max_uncles"], suffixes=("_c", "_o")) @@ -150,10 +164,18 @@ def main() -> None: out = Path(args.out) out.mkdir(parents=True, exist_ok=True) - cnt, old = _cells(_load(args.countable)), _cells(_load(args.old)) + cnt_raw = _load(args.countable) + cnt, old = _cells(cnt_raw), _cells(_load(args.old)) g = gaps(cnt, old) prov = "tsi-sim-pernode fine-delay.yaml (+--old)" + # rho per delay, derived (never hand-substituted) — these are the report's axis labels. + delays = sorted(cnt[DELAY].unique()) + print("load rho = f*D_vis per delay (measured ell_mean, see figures_pernode.rho_for):") + print(" " + " ".join(f"delay={d:g}: rho={r:.3f}" + for d, r in zip(delays, rho_for(cnt_raw, delays), strict=True))) + print() + written = [] written += style.save(fig_accuracy(cnt, old), out / "fine_accuracy_vs_delay", prov) written += style.save(fig_gap(g), out / "fine_gap_vs_delay", prov) @@ -193,6 +215,18 @@ def main() -> None: print(f"\nU=0 negative control (true gap = 0): |gap| up to {ctl.gap.abs().max():.4f}, " f"max t = {ctl.t.max():.2f}, 95% CI +-{ctl.ci95.max():.4f} " f"-> control {'PASSES' if ctl.t.max() < 2 else 'FAILS'}") + + # Absolute test: does uncle recovery actually land on 1.0? Same question as the gap + # test, asked without reference to the other model. + for lbl, cells in (("countable", cnt), ("unrestricted", old)): + v = vs_one(cells) + lo = v[v.t <= -2] + print(f"\nvs exact 1.0, {lbl}: {len(lo)}/{len(v)} cells significantly BELOW 1") + if len(lo): + for d, s in lo.groupby(DELAY): + caps = "/".join(f"U={int(x)}" for x in sorted(s.max_uncles)) + print(f" delay={d:>4g}: {caps} dev {s.dev.min():+.5f}..{s.dev.max():+.5f} " + f"t {s.t.min():.2f}..{s.t.max():.2f}") print(f"wrote {len(written)} files -> {out}") diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py index c293eb1..66319b8 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/rho_boundary_analysis.py @@ -21,33 +21,14 @@ import pandas as pd sys.path.insert(0, str(Path(__file__).resolve().parents[1] / "src")) -from tsi_sim.config import SimConfig # noqa: E402 from tsi_sim.plotting import style # noqa: E402 -from tsi_sim.topology import build_path_latency # noqa: E402 +from tsi_sim.plotting.figures_pernode import graph_ell_mean # noqa: E402 HERE = Path(__file__).resolve().parent.parent RUNS = HERE / "runs" FIGS = HERE / "report-figures" -def graph_ell_mean(df: pd.DataFrame) -> float: - """``ell_mean`` — the mean shortest-path (gossip) latency of the run's OWN peering graph. - - Measured from the run's recorded ``(n_nodes, degree, link_latency_mean, link_latency_dist)`` - rather than hardcoded, so the rho axis stays correct if any of those change. It is a statistical - property of the random d-regular geo graph (seed-invariant to <1% at this N), so one - representative draw suffices. Post-processing only — this rebuilds the latency *graph* to read - off its mean, and never touches or re-runs the simulation. - """ - row = df.iloc[0] - cfg = SimConfig(n_nodes=int(row.n_nodes), degree=int(row.degree), topology="blend", - link_latency_mean=float(row.link_latency_mean), - link_latency_dist=str(row.link_latency_dist), k=int(row.k)) - pl = build_path_latency(cfg, np.random.default_rng(0)) - n = pl.shape[0] - return float(pl[~np.eye(n, dtype=bool)].mean()) - - def load() -> pd.DataFrame: src = sorted(RUNS.glob("*_rho-boundary/results.parquet"))[-1] df = pd.read_parquet(src) diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py index dfad269..7843d86 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/plotting/figures_pernode.py @@ -48,6 +48,41 @@ def recovery_rate(q, q_u): return (q_u - q) / np.maximum(1.0 - q, 1e-12) +def graph_ell_mean(df: pd.DataFrame) -> float: + """``ell_mean`` — the mean shortest-path (gossip) latency of the run's OWN peering graph. + + Measured from the run's recorded ``(n_nodes, degree, link_latency_mean, + link_latency_dist)`` rather than hardcoded, so any derived quantity stays correct if + those change. A statistical property of the random d-regular geo graph (seed-invariant + to <1% at these N), so one representative draw suffices. Post-processing only: this + rebuilds the latency *graph* to read off its mean and never re-runs the simulation. + """ + from ..config import SimConfig + from ..topology import build_path_latency + + row = df.iloc[0] + cfg = SimConfig(n_nodes=int(row.n_nodes), degree=int(row.degree), topology="blend", + link_latency_mean=float(row.link_latency_mean), + link_latency_dist=str(row.link_latency_dist), k=int(row.k)) + pl = build_path_latency(cfg, np.random.default_rng(0)) + n = pl.shape[0] + return float(pl[~np.eye(n, dtype=bool)].mean()) + + +def rho_for(df: pd.DataFrame, delay) -> np.ndarray: + """Load ``rho = f * D_vis`` with ``D_vis = hops*delta_max/2 + (hops+1)*ell_mean``. + + Every report quotation of ``rho`` must come through here. ``ell_mean`` is the MEASURED + mean gossip latency (1.21 slots at N=1000/degree=6), not the per-link + ``link_latency_mean`` parameter (0.5) — using the latter understates ``rho`` by ~0.1, + and hand-substituting a guessed value is how wrong axis labels get into a report. + """ + f = float(df.f.iloc[0]) + hops = int(df.blend_hops.iloc[0]) + ell = graph_ell_mean(df) + return f * (hops * np.asarray(delay, dtype=float) / 2.0 + (hops + 1) * ell) + + def _lat_axis(topo: str) -> tuple[str, str]: """(dataframe column, axis label) for the dominant latency knob of a graph topology.""" if topo == "blend": From c5059c2fc8886a4bfccdc7b9aa3b64fc871b496a Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Wed, 5 Aug 2026 10:42:03 +0200 Subject: [PATCH 05/22] Consolidate the TSI report into one document MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The four-part split existed because the single report had grown dense and heavily cross-referenced; splitting traded that for a different cost, which the merged read makes visible. Section numbers (§1–§9, Appendices A–C) were already the stable identifiers, so the parts were a packaging choice, not a structural one. reports/tsi/tsi-report.md is now the whole report. Parts are interleaved back into section order — §1, §2–§5, §6, §7–§8, §9 + appendices — which is NOT concatenation order: Part 1 carried §1, §7 and §8, so appending files in sequence would have put §7–§8 ahead of §2. Every cross-file link collapses to an internal anchor; all 47 anchors resolve, all 37 figure embeds resolve, and no line of prose was lost (verified by diffing normalised content lines with link targets stripped — 0 lost, additions are the new header and table of contents). Coherence fixes the merge exposed, all artefacts of the split: - The roadmap paragraph described "four parts (see the index)" and is now a section-order roadmap, with its circular self-link to §1 dropped. - §7's figure-location note pointed readers at "the other parts". It now names the actual sections, and it was also WRONG about three figures: fig17/fig18/fig21 are in Appendix C and figB1/figB2 in Appendix B, not §9. It had also never been updated for fig30–fig35. - §9's "throughout this part" is now "throughout". README.md becomes a proper index — a section table pointing into the one document — rather than a list of four files. scripts/split_report.py is deleted: a one-time migration that produced the split, now both obsolete and pointing the wrong way. scripts/build_html.py was already broken before this change — it still read the report from tsi-sim-pernode/, where the files stopped living when they moved to reports/tsi/. Retargeted at reports/tsi/ and the single document; verified end-to-end (0 broken internal anchors, 0 unrewritten .md links, 37 images in the rendered HTML). Its output is now gitignored, as its docstring always claimed it was. Co-Authored-By: Claude Opus 5 (1M context) --- .gitignore | 3 + reports/tsi/README.md | 28 +- ...i-report-1-overview-and-recommendations.md | 191 ---- .../tsi/tsi-report-2-accuracy-and-design.md | 375 ------- .../tsi-report-3-robustness-and-incentives.md | 246 ----- ...report-4-reproducibility-and-appendices.md | 146 --- reports/tsi/tsi-report.md | 943 ++++++++++++++++++ .../tsi/tsi-sim-pernode/scripts/build_html.py | 26 +- .../tsi-sim-pernode/scripts/split_report.py | 214 ---- 9 files changed, 977 insertions(+), 1195 deletions(-) delete mode 100644 reports/tsi/tsi-report-1-overview-and-recommendations.md delete mode 100644 reports/tsi/tsi-report-2-accuracy-and-design.md delete mode 100644 reports/tsi/tsi-report-3-robustness-and-incentives.md delete mode 100644 reports/tsi/tsi-report-4-reproducibility-and-appendices.md create mode 100644 reports/tsi/tsi-report.md delete mode 100644 tools/simulators/tsi/tsi-sim-pernode/scripts/split_report.py diff --git a/.gitignore b/.gitignore index 559613b..bc74d7e 100644 --- a/.gitignore +++ b/.gitignore @@ -224,3 +224,6 @@ __marimo__/ # External upstream clones vendored for benchmarking (own .git, not our history) tools/benchmarks/original/ + +# Rendered report HTML — a build artifact of scripts/build_html.py; markdown is the source +reports/**/*.html diff --git a/reports/tsi/README.md b/reports/tsi/README.md index fb9afd5..2a29add 100644 --- a/reports/tsi/README.md +++ b/reports/tsi/README.md @@ -2,20 +2,30 @@ *Per-node network simulation of Cryptarchia Total Stake Inference (TSI). Simulator: [`tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode). All runs at the true security parameter **k = 2160** unless noted; latency is in slots and **1 slot = 1 s**.* -This report selects and justifies the TSI parameters for Cryptarchia from a per-node network simulation. It is split into four cohesive parts; section numbers (§1–§9, A–C) are stable identifiers preserved across the set. +This report selects and justifies the TSI parameters for Cryptarchia from a per-node network simulation. The whole report is one document — **[tsi-report.md](tsi-report.md)** — and section numbers (§1–§9, Appendices A–C) are stable identifiers referenced from the simulator and from spec discussion. -> **Uncle references.** The model analysed throughout is the **countable** one: counting-only references, deduplicated by slot, drawn from first-fork blocks only, within a window derived as `w_u = W_abs/f`. An **unrestricted** baseline — any orphan in the window at any fork depth — is measured alongside it for comparison. The two are indistinguishable in the design regime `ρ < 1` and diverge only under overload. See the model note at the top of [Part 1](tsi-report-1-overview-and-recommendations.md), the mechanism in [§2.1](tsi-report-2-accuracy-and-design.md#s2-1), the comparison in [§3.2](tsi-report-2-accuracy-and-design.md#s3-2)–[§3.2a](tsi-report-2-accuracy-and-design.md#s3-2a), and the reproduction notes in [§9](tsi-report-4-reproducibility-and-appendices.md#s9). +> **Uncle references.** The model analysed throughout is the **countable** one: counting-only references, deduplicated by slot, drawn from first-fork blocks only, within a window derived as `w_u = W_abs/f`. An **unrestricted** baseline — any orphan in the window at any fork depth — is measured alongside it for comparison. The two are indistinguishable in the design regime `ρ < 1` and diverge only under overload. See the model note at the top of the [report](tsi-report.md), the mechanism in [§2.1](tsi-report.md#s2-1), the comparison in [§3.2](tsi-report.md#s3-2)–[§3.2a](tsi-report.md#s3-2a), and the reproduction notes in [§9](tsi-report.md#s9). -## Parts +## Contents -1. **[Overview and recommendations](tsi-report-1-overview-and-recommendations.md)** — the executive summary, the per-knob parameter reference (§7), and the safest selection with residual risks and the recommendation-vs-spec deltas (§8). -2. **[Accuracy and design](tsi-report-2-accuracy-and-design.md)** — the model and counting rule (§2), the seven findings and their evidence (§3), the design equations and selection algorithm (§4), and the caveats and regime of validity (§5). -3. **[Robustness and incentives](tsi-report-3-robustness-and-incentives.md)** — jitter, grinding, withholding, selfish mining, the reward design, fork/reorg depth, and organic churn (§6). -4. **[Reproducibility and appendices](tsi-report-4-reproducibility-and-appendices.md)** — how to re-run every study (§9), the residual f-rounding offset (App A), the per-epoch noise floor (App B), and consensus detail (App C). +**[Read the report →](tsi-report.md)** + +| § | what it covers | +|---|---| +| [§1](tsi-report.md#s1) | executive summary — the problem, the findings, the recommendation | +| [§2](tsi-report.md#s2) | the model, the measurement convention, and the counting rule | +| [§3](tsi-report.md#s3) | the findings and their evidence, including the high-precision design band ([§3.2a](tsi-report.md#s3-2a)) | +| [§4](tsi-report.md#s4) | design equations and the parameter-selection algorithm | +| [§5](tsi-report.md#s5) | caveats and regime of validity | +| [§6](tsi-report.md#s6) | robustness — jitter, grinding, withholding, selfish mining, rewards, reorg depth, churn | +| [§7](tsi-report.md#s7) | parameter reference — what each knob does | +| [§8](tsi-report.md#s8) | the safest selection, residual risks, and the recommendation-vs-spec deltas | +| [§9](tsi-report.md#s9) | reproducibility — how to re-run every study | +| [A](tsi-report.md#sA) · [B](tsi-report.md#sB) · [C](tsi-report.md#sC) | the residual `f`-rounding offset · the per-epoch noise floor · consensus detail | ## Headline recommendation -Cryptarchia baseline f = 1/30. Two design choices are foundational: count uncles **per occupied slot**, not per block — the density-bug fix that lands the estimate at exactly `D` ([§2.1](tsi-report-2-accuracy-and-design.md#s2-1), [§8.5](tsi-report-1-overview-and-recommendations.md#s8-5)) — and make genesis `D̂` **a single protocol constant, identical at every node**, never client-configurable, since a per-node divergence is never self-corrected ([§8.1](tsi-report-1-overview-and-recommendations.md#s8-1) row 7). The settings: security `k = 2160`, uncle window `W = 300` slots, uncle cap `U ≥ ⌈ρ⌉ + 1` (2 at the Blend target; the protocol's `MAX_UNCLES = 4` sits safely above it), learning rate `β = 1`, on-chain `f` at 10⁻⁶ precision, peering degree ≥ 6 at scale, soft uncle rewards with `w_u + w_n < 1`, and operate at load `ρ = f·D_vis < 1`. The full recommended-configuration table and rationale are in **[Part 1 →](tsi-report-1-overview-and-recommendations.md)**. +Cryptarchia baseline f = 1/30. Two design choices are foundational: count uncles **per occupied slot**, not per block — the density-bug fix that lands the estimate at exactly `D` ([§2.1](tsi-report.md#s2-1), [§8.5](tsi-report.md#s8-5)) — and make genesis `D̂` **a single protocol constant, identical at every node**, never client-configurable, since a per-node divergence is never self-corrected ([§8.1](tsi-report.md#s8-1) row 7). The settings: security `k = 2160`, uncle window `W = 300` slots, uncle cap `U ≥ ⌈ρ⌉ + 1` (2 at the Blend target; the protocol's `MAX_UNCLES = 4` sits safely above it), learning rate `β = 1`, on-chain `f` at 10⁻⁶ precision, peering degree ≥ 6 at scale, soft uncle rewards with `w_u + w_n < 1`, and operate at load `ρ = f·D_vis < 1`. The full recommended-configuration table and rationale are in **[§8 →](tsi-report.md#s8)**. ## Figures @@ -23,4 +33,4 @@ Figures are embedded from [`report-figures/`](report-figures) via relative links ## Reproducing the results -The simulation code, configs, and run data live in [`tools/simulators/tsi/tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode). Every study's exact command is listed in [Part 4 — Reproducibility (§9)](tsi-report-4-reproducibility-and-appendices.md). In short, from the simulator directory: `make install`, then `make ` to run a sweep (results land under `runs/_

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z6?){cM-B{*&0}3NU2YV=_8suS(Q-hSTe@mxVn-g@s942>Soa-499c|lX@T}2t#JTn zad_lgC=tu!(cb)6*I-CNRcc$fBwZ9HpeIT(FDHOk%x=HI?khXlxRuak#*eC8O79N= z3*B-hKj&dn@*N6f{>shg%t>m{|CUN(n{T{u$D7~etw9SbT_7N#N`sBj&R?FNAl~m4 zih;h7ImF6}1G|*j7yuzhL`xT%XPpg9)nK9#3-7EOxXYw5^MTC&?=|}T3^EXcrBS3B zI~6g?WoCJk-VxO(`aE9bRStV2qW}0z6no}2S38bj5BR{lG_gfVBt>t~yUgh{iyYpV}dM(i(<(^{l&{_^qu zTBxer^M9>@CE+|{J-F+R+pZ_tnssZP88yRMI!Atj?ZurbVIJ?6Z}b7L`d8xJOYLRtCrYl^@P}=lEHAQ~SC! z*I7&B;dK{W&1WXhw9JB19iMjjyuXgiMk|<=NthtAo|L2_-<|+*>-uUIb8xPGarpBr zN0pAX;fPUW$lc>wZd0|eV z8*}q{1SiVS5}#T%JxOnI&pW@!#9lSn0f6V#z3nIw)q>ywA^vSg)W@ZeZWkxdh+L`& zHaxIm`C}Bv>dr)^TZ&R=)>V2{Bp^UxNPRE~Eh#c>9h|glk@n_P^re%tgP2g{Bag#LezaGKvmjIERM@!hLKC8yjNW*#%u z)rvFkt&2I0<`Dgru<4QI?-P0#plOXuvU*wF2^B~9{B*09NKJVw4=93_Lz0~eT zF=D7hw$%a>1+C~Y$KS<#=g`P0FT}^zTWq89(&K+-fM^cWGV|FYO)L_&-!{Wz3f4zm zKn6FkL2}Q<$QmZ~|6{ru&4Y-j6aRe_@cDni_ **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](#s6-7)–[§6.8](#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](#s2-1), [§3.2](#s3-2), [§9](#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.21–0.41`) puts every `U ≥ 1` cell of both models in 0.998–1.001, resolves no difference in any individual cell (widest 95 % CI ±0.15 pp), and bounds the first-fork cost at **≤ 0.2 %** — statistically indistinguishable from zero up to `δ_max = 4`, and resolved only at the top of the band, where it is ~0.14 % ([§3.2a](#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. +> **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](#s6-7)–[§6.8](#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](#s2-1), [§3.2](#s3-2), [§9](#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate **paired** sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.21–0.41`), in which both arms share the stake draw, the peering graph and every lottery outcome so the uncle rule is the only difference, puts every `U ≥ 1` cell of both models in 0.998–1.001 and pins the first-fork cost at **nothing measurable up to `δ_max` = 3 and ~0.1 % at `δ_max` = 4–5** ([§3.2a](#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. ## 1. Executive summary @@ -193,35 +193,33 @@ So: **at the operating loads (`ρ < 1`) no difference between the models is dete ### 3.2a The design band at high precision — `δ_max` 1–5 -**The question.** [§3.2](#s3-2) samples the mixing delay at 4/8/16/32. That resolves the overload regime, but it leaves the band the parameters are actually chosen in — the low-delay end, where every operating point sits — measured at four-fold spacing and five replicates, which is enough to say "no difference detected" and nothing more. How accurate is TSI across `δ_max` = 1–5, and how large a first-fork cost can be *excluded* there? +**The question.** [§3.2](#s3-2) samples the mixing delay at 4/8/16/32 with five replicates. That resolves the overload regime, but it leaves the band the parameters are actually chosen in measured at four-fold spacing and low power — enough to say "no difference detected" and nothing more. How accurate is TSI across `δ_max` = 1–5, and how large a first-fork cost can be *excluded* there? -**The finding.** One uncle slot holds the estimate at the true stake across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay, while the uncle-free baseline decays 0.810 → 0.640. The two referencing models are **indistinguishable through `δ_max` ≤ 3**; at the top of the band the first-fork restriction becomes measurable and costs **0.1–0.2 %**. Only the `δ_max = 5` result is statistically resolved; the weaker claims below are labelled as such. +**The finding.** One uncle slot holds the estimate at the true stake across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay, while the uncle-free baseline decays 0.806 → 0.623. The first-fork restriction costs **nothing measurable up to `δ_max` = 3** and about **0.1 %** at `δ_max` = 4–5. -`configs/fine-delay.yaml` spends replicates instead of range — `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, **40 replicates** per cell (8× [§3.2](#s3-2)), N = 1 000, blend, 3 hops — run under both models ([§9](#s9)). The band spans `ρ ≈ 0.21` to `0.41`, entirely inside the design regime. +**The design is paired.** The two referencing models normally draw independent RNG streams — `uncle_model` is part of the config key, which is what lets `--old` bit-reproduce earlier runs ([§9](#s9)) — so a comparison pays the between-run variance twice and the arms differ in stake draw, peering graph and every lottery outcome. `configs/fine-delay-paired.yaml` sets `paired_streams`, which derives the RNG root from the model-independent part of the key: both arms then get the **same stake, the same graph and the same lottery draws**, and the uncle rule is the only difference. Each replicate becomes a matched pair, the shared variance cancels, and the test is a one-sample t on the 40 per-replicate differences. Trajectories still diverge after epoch 0 through the genuine feedback — a different counted density changes the next epoch's difficulty — which is the effect being measured, not noise. Grid: `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, 40 replicates, N = 1 000, blend, 3 hops, spanning `ρ ≈ 0.21` to `0.41`. -| `δ_max` (s) | ρ | `U=0` countable / unrestricted | `U≥1` countable | `U≥1` unrestricted | pooled gap (t) | +| `δ_max` (s) | ρ | `U=0` (both models) | `U≥1` countable | `U≥1` unrestricted | pooled gap (t) | |---|---|---|---|---|---| -| 1 | ≈ 0.21 | 0.810 / 0.806 | 0.9994 – 0.9999 | 0.9990 – 1.0010 | −0.0004 ± 0.0007 (1.1) | -| 2 | ≈ 0.26 | 0.762 / 0.763 | 0.9996 – 1.0002 | 0.9996 – 1.0003 | +0.0000 ± 0.0008 (0.0) | -| 3 | ≈ 0.31 | 0.716 / 0.723 | 0.9995 – 1.0002 | 0.9992 – 1.0004 | −0.0001 ± 0.0008 (0.2) | -| 4 | ≈ 0.36 | 0.664 / 0.668 | 0.9988 – 0.9996 | 0.9995 – 0.9999 | −0.0005 ± 0.0008 (1.3) | -| 5 | ≈ 0.41 | 0.640 / 0.623 | 0.9982 – 0.9988 | 0.9995 – 1.0003 | **−0.0014 ± 0.0007 (3.7)** | +| 1 | ≈ 0.21 | 0.806 | 0.9995 – 1.0004 | 0.9990 – 1.0010 | −0.0003 ± 0.0005 (1.1) | +| 2 | ≈ 0.26 | 0.763 | 0.9993 – 0.9996 | 0.9996 – 1.0003 | −0.0004 ± 0.0005 (1.8) | +| 3 | ≈ 0.31 | 0.723 | 0.9993 – 0.9997 | 0.9992 – 1.0004 | −0.0003 ± 0.0004 (1.4) | +| 4 | ≈ 0.36 | 0.668 | 0.9982 – 0.9997 | 0.9995 – 0.9999 | **−0.0011 ± 0.0004 (4.7)** | +| 5 | ≈ 0.41 | 0.623 | 0.9986 – 0.9992 | 0.9995 – 1.0003 | **−0.0009 ± 0.0005 (3.7)** | -**No individual cell resolves a model difference.** Across the 15 `U ≥ 1` cells the widest 95 % CI half-width is ±0.0015, one cell clears `t = 2` (0.75 are expected to by chance), and its `t = 2.59` does not survive the Bonferroni threshold of 2.94 for 15 tests. Read cell by cell, the honest statement is that any difference is **smaller than ±0.15 pp**. +**The negative control is now an identity check.** With `U = 0` no reference is ever taken, so under shared streams the two arms must produce *bit-identical* trajectories — not merely agree within noise. They do: **all 200 replicate pairs differ by exactly 0.0**, at every delay. That is a far stronger validation than the unpaired design could offer, where the same control only had to agree within a ±0.025 band and in fact drifted by 0.016. -**Pooled, a delay-dependent cost appears at the top of the band.** The three uncle caps are separate draws (each `(δ_max, U, replicate)` cell is its own RNG stream, and the peering graph re-rolls with it), so inverse-variance pooling across them buys ~√3 in precision. Pooled per delay, `δ_max` 1–4 stay unresolved (|t| ≤ 1.3) while **`δ_max = 5` resolves at −0.0014 ± 0.0007 (t = 3.7)**. That one result is robust: a 20 000-draw permutation test on the same cells, assuming no distributional form, gives **p = 0.0003** (all other delays: p ≥ 0.21), and it survives Bonferroni correction for **every one of the 51 tests reported in this section** (threshold z = 3.30). Two weaker statements should not be read as resolved: the whole-band pooled gap, −0.00048 ± 0.00033 (t = 2.8), **fails** that same correction, and the sign imbalance (11 of 15 cells negative) is p = 0.12 on its own. A weighted regression of gap on delay — one pre-specifiable test, no choice of which delay to look at — gives a slope of −0.00024 ± 0.00012 per slot (t = −2.05): consistent with a monotone cost, but on its own marginal. The defensible reading is that the first-fork restriction costs nothing measurable up to `δ_max = 4` and about 0.14 % at `δ_max = 5`, which is negligible against the ±0.9 % per-epoch sampling noise of [Appendix B](#sB). (Pooling across `U` was chosen after inspecting the per-cell results; it is reported here because the `δ_max = 5` result survives the harshest correction available, not because the pooling was pre-registered.) +**What pairing bought.** Per-cell standard errors shrink by a median factor of 1.6 (range 1.2–2.1), taking the widest 95 % CI from ±0.0015 to **±0.0010**. Five of the fifteen `U ≥ 1` cells now resolve at |t| ≥ 2 against 0.75 expected by chance, and the largest (`U = 2`, `δ_max = 4`, t = 4.32) clears the Bonferroni threshold of 2.94 for 15 tests. The unpaired sweep resolved only `δ_max = 5`, and only after pooling. -**The same data, measured against 1.0 rather than against the other arm.** Dropping the unrestricted arm and asking whether each cell's equilibrium is exactly 1.0 removes one noisy measurement, so it is ~1.4× more sensitive. It is **not independent evidence** — it shares the countable arm with the gap test, and the two are correlated at ρ ≈ 0.73 — but the *contrast between the arms* is informative. Under the **unrestricted** model 1 of 15 cells sits below 1 (`t` = −2.09), consistent with chance. Under the **countable** model 4 of 15 do, and they are not scattered: `δ_max = 4` at `U = 1` (−0.0012, `t` = −2.6) and **all three uncle caps at `δ_max = 5`** (−0.0012 to −0.0019, `t` = −2.5 to −3.7; the `U = 2` cell survives the 51-test correction). A shortfall appearing at every cap at once, only at the top of the band, and only under the restricted model, is the signature of the first-fork cost rather than of noise. +**The cost is a step, not a ramp.** Pooling across the three uncle caps — separate draws of the same underlying difference — `δ_max` 1–3 stay unresolved (t = 1.1, 1.8, 1.4) and then **`δ_max` = 4 and 5 both resolve**, at −0.0011 (t = 4.7) and −0.0009 (t = 3.7). Over the whole band the pooled gap is −0.00060 ± 0.00021, **t = 5.7** — comfortably resolved, where the unpaired estimate of the same quantity (t = 2.8) did not survive correction. So the restriction switches on somewhere around `δ_max` ≈ 4 rather than growing smoothly with delay, and above that it sits near 0.1 % without deepening across the band tested. Measured against the exact target 1.0 instead of against the other arm — a more sensitive view of the same countable data, not independent evidence — the same picture appears: the unrestricted model has 1 of 15 cells below 1 (chance), the countable model has 5, all at `δ_max` 4–5. -**What limits the resolution: the comparison is unpaired.** The two models draw independent RNG streams by construction (`uncle_model` enters the config key, which is what makes `--old` bit-reproduce the earlier runs, [§9](#s9)), so a countable replicate and an unrestricted replicate share neither the peering graph nor the lottery draws. Every comparison therefore pays the full between-run variance twice, and at 40 replicates that floor is ±0.0015 per cell — an order of magnitude above the effect being measured. A **paired** design — same graph, same lottery outcomes, the uncle rule the only difference — would cancel almost all of that shared variance and could resolve the per-cell effect directly instead of only after pooling. It would require seeding the graph and lottery from topology-only entropy, and re-running both arms; it is the single change that would most improve this measurement, and it is not done here. +**How big is 0.1 %.** An order of magnitude below the ±0.9 % per-epoch sampling noise of [Appendix B](#sB), and below the ~1 % fixed-point rounding bias of [Appendix A](#sA). The [§1](#s1) statement that one uncle restores the estimate to the true stake holds at the precision that matters; this section puts the residual at ~0.1 % at the top of the band rather than at zero. -**The negative control passes.** The `U = 0` arms — identical models by construction — show |gap| ≤ 0.016 with max `t` = 1.26, i.e. no spurious signal, but a 95 % CI of ±0.025: **17× wider than the entire `U ≥ 1` range.** The unrecovered regime is intrinsically noisy, which is precisely why the model comparison has to be made where uncles are active. +![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap under common random numbers, error bars = replicate SEM over 40 pairs: every U ≥ 1 curve sits at 1.000 across the band under both models (to within 0.2 %), while U = 0 — the negative control — decays 0.81 → 0.62 identically for both.](report-figures/fig34_fine_delay_accuracy.png) -![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM over 40 replicates: every U ≥ 1 curve sits at 1.000 across the band under both models (to within 0.2 %), while U = 0 — the negative control — decays 0.81 → 0.64.](report-figures/fig34_fine_delay_accuracy.png) +![Fig 35 — the paired countable − unrestricted gap with 95% CIs, with the inverse-variance pooled estimate in black: flat and unresolved through δ_max = 3, then a resolved ~0.1 % cost at δ_max = 4 and 5.](report-figures/fig35_fine_delay_gap.png) -![Fig 35 — the countable − unrestricted gap with 95% CIs, zoomed to the U ≥ 1 scale, with the inverse-variance pooled estimate in black: no single cell resolves, the pooled trend is monotone in delay, and only δ_max = 5 separates from zero (−0.0014 ± 0.0007).](report-figures/fig35_fine_delay_gap.png) - -**What this settles.** One uncle slot is sufficient everywhere in the operating band under either referencing model — the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.41`, and raising `U` past 1 buys nothing here (at `δ_max = 5` all three caps sit at the same 0.1–0.2 % shortfall, so the residual is *not* a capacity limit). And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **at most 0.2 %** anywhere a deployment should be operating — an order of magnitude below the ±0.9 % per-epoch sampling noise of [Appendix B](#sB), and below the ~1 % fixed-point rounding bias of [Appendix A](#sA). The [§1](#s1) statement that one uncle restores the estimate to the true stake holds at the precision that matters; this section puts the residual at 0.1–0.2 % at the top of the band rather than zero. +**What this settles.** One uncle slot is sufficient everywhere in the operating band under either referencing model — the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.41`, and raising `U` past 1 does not remove the residual (all three caps show the same ~0.1 % shortfall at `δ_max` = 4–5, so it is not a capacity limit). And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **about 0.1 %** at the top of the design band and nothing measurable below it. ### 3.3 One uncle is not always enough — the load `ρ` @@ -845,14 +843,15 @@ Sweep studies are committed configs, run with `make ` (writes a dated `run | U = 0 fluctuation series (zero delay, k ∈ {256, 1024, 2160}) | `scripts/appendix_fluct.py --run` (`runs/fluctuation_u0.parquet`) | [Appendix B](#sB) | | CI smoke grid + analytic sanity checks | `configs/smoke.yaml`; `scripts/verify.py` (`make verify`) — validation only, no figures | — | | **countable vs unrestricted referencing** (accuracy over delay × U; measured `q_u`/recovery `r`) | `configs/countable-vs-old.yaml` run twice — default and with `--old`; figures + significance table by `scripts/plot_countable_vs_old.py` | [§2.1](#s2-1), [§3.2](#s3-2) | -| **fine delay band** (δ_max 1–5 at 40 replicates; tight CI on the model gap in the design regime) | `configs/fine-delay.yaml` run twice — default and with `--old`; figures + significance tables (model gap, and each model vs the exact 1.0 target) by `scripts/plot_fine_delay.py` | [§3.2a](#s3-2a) | +| **fine delay band, PAIRED** (δ_max 1–5, 40 replicates, common random numbers — the primary design-regime measurement) | `configs/fine-delay-paired.yaml` run twice — default and with `--old`; paired-difference tests + figures by `scripts/plot_fine_delay.py` | [§3.2a](#s3-2a) | +| fine delay band, unpaired (same grid without `paired_streams`; superseded, retained as the power comparison) | `configs/fine-delay.yaml` run twice | [§3.2a](#s3-2a) | | **window absorption sweep** (`W` in expected block-intervals, `w_u = W/f` derived) | `configs/absorption-window.yaml`; figure by `scripts/plot_countable_vs_old.py` | [§3.4](#s3-4) | **Uncle-model convention.** The simulator's default is the **countable** model — first-fork candidates only, derived window `w_u = W/f`, occupied-slot exclusion, per-reference counting rules ([§2.1](#s2-1)). The **unrestricted** baseline is preserved in the code and selected with `--old` on `tsi-sweep`/`tsi-verify`. Its RNG key is byte-identical to the pre-restriction key, so `--old` **bit-reproduces the earlier runs**: a `rho-boundary` cell (δ_max = 8, U = 2, k = 256, N = 1 000) re-run under `--old` matches the committed `2026-07-27_195627_rho-boundary` parquet with `max |Δ| = 0` on every epoch and every metric. Studies in the table above that predate the countable default were produced under the unrestricted model and reproduce exactly under `--old`; the comparison rows quantify where the two models differ, and in the design regime (`ρ < 1`) no difference is resolvable, so those findings carry over unchanged. Because the two models draw independent RNG streams, every countable-vs-unrestricted comparison is **unpaired**, and its resolution is set by the replicate spread rather than by the effect size. Each comparison sweep therefore includes a `U = 0` arm as a **negative control**: with no uncles the models are identical by construction, so the measured `U = 0` gap is a direct reading of the noise floor at that delay and replicate count. At `δ_max = 32` with 5 replicates that floor is ≈ 0.23 in `D̂/D` — larger than several real effects elsewhere in the grid — which is why [§3.2](#s3-2) reports a `t` statistic per cell and why the design regime is measured separately at 40 replicates ([§3.2a](#s3-2a)). -All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. Referencing-model studies: countable-vs-unrestricted = `2026-08-04_103536_cvo-countable` / `2026-08-04_104010_cvo-old`; window absorption = `2026-08-04_104633_absorption-window`; fine delay band = `2026-08-04_191441_fine-countable` / `2026-08-04_195353_fine-old`. +All studies were **re-run on 2026-07-23/24 with the corrected slot-counting mechanism** ([§2.1](#s2-1)) and the early-stop optimisation; the resilient batch is `scripts/run_all_reruns.sh` (per-step log in `runs/rerun_status.log`). Canonical run directories (latest): fullscale N=5000/10000 = `2026-07-24_094519_fullscale`; fullscale N=1000/2000 = `2026-07-23_171803_fullscale-small`; uncle-window = `2026-07-24_001456`; window-uncles = `2026-07-24_014240`; block-rate = `2026-07-24_043943`; blend-hops-delay = `2026-07-24_064052`; window-scale = `2026-07-24_085234`; latency-shape = `2026-07-24_090014_expdist`; stake-tail = `2026-07-24_090044_pareto133`; heterogeneous-start = `2026-07-24_090114_default`; N-scaling = the `nscaling-{a,b}` + `nscaling32-{a,b}` runs; adversary grids = `runs/adversary_grid/`; jitter = `runs/jitter_grid/`; bootstrap = `runs/bootstrap_fullscale/`; fluctuation = `runs/fluctuation_u0.parquet`; fork-rate = `runs/fork_rate_vs_delay.parquet`; ρ-boundary = `2026-07-27_195627_rho-boundary`. Referencing-model studies: countable-vs-unrestricted = `2026-08-04_103536_cvo-countable` / `2026-08-04_104010_cvo-old`; window absorption = `2026-08-04_104633_absorption-window`; fine delay band (unpaired) = `2026-08-04_191441_fine-countable` / `2026-08-04_195353_fine-old`; fine delay band (paired, primary) = `2026-08-05_111109_fine-paired-countable` / `2026-08-05_113218_fine-paired-old`. Figures are in `report-figures/` (`fig1`–`fig29`, plus [Appendix B](#sB)'s `figB1`–`figB2`; numbering is generation order, not order of appearance). Committed generators: `fig1` (bootstrap, k=2160) by `scripts/bootstrap_dynamics.py`; `fig2`,`fig4`,`fig5`,`fig17`–`fig22` by `scripts/regenerate_extra_figs.py` from the latest sweeps (`fig3` hops×delay×U grid by `scripts/hops_delay_grid.py`, `fig6` (block-rate `U_min` grid + ρ-collapse) rendered ad hoc from `runs/2026-07-24_043943_block-rate` with no committed generator; `fig26` deficit-vs-ρ by `scripts/rho_boundary_analysis.py`) (fullscale-derived `fig17`–`fig20` pool both sizes in that run, N = 5 000 and N = 10 000 — the generators filter on stake_dist/topology/degree/init_dest only, never on `n_nodes`); `fig8`,`fig9` by `scripts/adversary_figs.py` from `runs/adversary_grid/`; `fig10`–`fig12` by `scripts/dynamic_withhold.py`; `fig13`–`fig15` by `scripts/selfish_mining.py`/`selfish_rewards.py`/`reward_mandate.py`; `fig16` by `scripts/stake_vs_delay.py`; `fig23`–`fig24` by `scripts/nscaling_analysis.py`; `fig25` by `scripts/window_scale_analysis.py`; `fig27`–`fig28` by `scripts/reorg_depth.py` (fork rates via `--measure`; private-chain model `src/tsi_sim/reorg.py`); `fig29` by `scripts/churn.py`; `figB1`–`figB2` by `scripts/appendix_fluct.py`. `fig7` (feedback fixed-point) is an analytic overlay; `fig30`–`fig33` (countable-vs-unrestricted accuracy, `q_u`-prediction check, recovery rate, absorption-window sweep) by `scripts/plot_countable_vs_old.py` from the `cvo-countable`/`cvo-old`/`absorption-window` runs; `fig34`–`fig35` (design-regime accuracy and the model gap with 95 % CIs) by `scripts/plot_fine_delay.py` from the `fine-countable`/`fine-old` runs. Every figure type the per-node simulator generates appears in this report, and the fork-rate/reorg-depth study closes the previous reproducibility gap for the adversarial figures (`fig8`,`fig9` now have committed generators from `runs/adversary_grid/`). diff --git a/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay-paired.yaml b/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay-paired.yaml new file mode 100644 index 0000000..255fc79 --- /dev/null +++ b/tools/simulators/tsi/tsi-sim-pernode/configs/fine-delay-paired.yaml @@ -0,0 +1,38 @@ +# PAIRED high-precision sweep of the low mixing-delay band (the design regime). +# +# Identical grid to fine-delay.yaml, but with paired_streams: true. The unpaired sweep pays the +# between-run variance twice — the two uncle models draw independent stake, graph and lottery +# streams — which puts a ~+-0.0015 per-cell floor on the countable-vs-unrestricted comparison, +# an order of magnitude above the effect. Only delta_max = 5 resolved there, and only after +# pooling across uncle caps. +# +# paired_streams drops the uncle-model marker from the RNG root, so a countable cell and its +# --old twin get the SAME stake draw, the SAME peering graph and the SAME lottery outcomes; +# the uncle rule is then the only difference and the per-replicate difference is a PAIRED +# observation. The shared variance cancels, so the paired test should resolve the per-cell +# effect directly. Trajectories still diverge after epoch 0 through the genuine feedback (a +# different counted density changes the next epoch's difficulty) — that is the signal. +# +# Run TWICE — default (countable) and with --old — same grid. U=0 remains the negative control: +# with no uncles AND a shared stream the two arms must now agree EXACTLY, which is a far +# stronger check than the unpaired version (there it only had to agree within noise). +# Latency is in SLOTS (1 slot = 1 s). +n_nodes: [1000] # network size +stake_dist: [pareto] # heavy-tailed (realistic) stake distribution +topology: [blend] # Blend mixnet (the multi-slot fork regime) +degree: [6] # peering degree of the d-regular graph +link_latency_mean: [0.5] # natural geographic transport (sub-slot) +link_latency_dist: [geo] # real-world geographic band mixture +blend_hops: [3] # fixed hop count; delay is the swept knob +blend_delay_max: [1.0, 2.0, 3.0, 4.0, 5.0] # THE fine region (integer slots) +max_uncles: [0, 1, 2, 4] # U: 0 = negative control, then the levers +uncle_strategy: [oldest] # spec selection: oldest-first fill +init_dest: [common] # per-node initial D_est from agreement +replicates: 40 # matches fine-delay.yaml for a like-for-like read +base: # per-run settings shared by every cell + k: 2160 # true security parameter + epochs: 20 # equilibrium within ~2 epochs; burn 50% + f: 0.03333333333333333 # slot activation coefficient (1/30) + genesis_d_factor: 0.5 # start near true stake (cheap epoch 0) + early_stop: true + paired_streams: true # common random numbers across the two arms diff --git a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py index a2a10e9..3750fb5 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py +++ b/tools/simulators/tsi/tsi-sim-pernode/scripts/plot_fine_delay.py @@ -46,6 +46,34 @@ def _load(run_dir: str | Path) -> pd.DataFrame: return pd.read_parquet(Path(run_dir) / "results.parquet") +def paired_gaps(cnt_raw: pd.DataFrame, old_raw: pd.DataFrame) -> pd.DataFrame | None: + """Per-replicate differences, when both arms were run with ``paired_streams``. + + Under common random numbers replicate *i* of each arm shares the stake draw, the peering + graph and the lottery outcomes, so ``d_i = countable_i - unrestricted_i`` is a PAIRED + observation and the shared variance cancels. The test is then a one-sample t on the d_i, + which is what makes a sub-0.1 % effect reachable per cell instead of only after pooling. + + Returns None when the runs are not paired, so the caller falls back to the unpaired test. + """ + if not (cnt_raw.get("paired_streams", pd.Series([False])).all() + and old_raw.get("paired_streams", pd.Series([False])).all()): + return None + c, o = equilibrium(cnt_raw), equilibrium(old_raw) + keys = [DELAY, "max_uncles", "replicate"] + m = c[[*keys, "mean_ratio"]].merge(o[[*keys, "mean_ratio"]], on=keys, + suffixes=("_c", "_o")) + m["d"] = m.mean_ratio_c - m.mean_ratio_o + rows = [] + for (dl, u), s in m.groupby([DELAY, "max_uncles"]): + d = s.d.to_numpy() + se = sem(d) + rows.append({DELAY: dl, "max_uncles": u, "gap": float(d.mean()), "se": se, + "ci95": Z95 * se, "t": abs(d.mean()) / se if se > 0 else np.inf, + "n_pair": len(d), "n_zero": int((d == 0.0).sum())}) + return pd.DataFrame(rows).sort_values(["max_uncles", DELAY]) + + def _cells(df: pd.DataFrame) -> pd.DataFrame: """Per (delay, U): replicate mean, SEM and count of the equilibrium accuracy.""" return equilibrium(df).groupby([DELAY, "max_uncles"], as_index=False).agg( @@ -146,10 +174,14 @@ def fig_gap(g: pd.DataFrame) -> plt.Figure: span = float(np.abs(np.r_[g[g.max_uncles > 0].gap + g[g.max_uncles > 0].ci95, g[g.max_uncles > 0].gap - g[g.max_uncles > 0].ci95]).max()) ax.set_ylim(-1.35 * span, 1.35 * span) - ax.text(0.015, 0.03, + # Under pairing the control is exactly 0 in every replicate pair (shared streams), so + # quoting a CI for it is meaningless; unpaired, the width of that CI is the point. + note = ("U=0 negative control: exactly 0.0 in all 200 replicate pairs " + "(shared streams — an identity check, not a noise check)" + if band == 0.0 else f"U=0 negative control (true gap = 0): 95% CI ±{band:.4f}, " - f"{band / span:.0f}× outside this range", - transform=ax.transAxes, fontsize=6.5, alpha=0.75) + f"{band / span:.0f}× outside this range") + ax.text(0.015, 0.03, note, transform=ax.transAxes, fontsize=6.5, alpha=0.75) ax.legend(fontsize="x-small", ncol=2) return fig @@ -164,10 +196,17 @@ def main() -> None: out = Path(args.out) out.mkdir(parents=True, exist_ok=True) - cnt_raw = _load(args.countable) - cnt, old = _cells(cnt_raw), _cells(_load(args.old)) - g = gaps(cnt, old) - prov = "tsi-sim-pernode fine-delay.yaml (+--old)" + cnt_raw, old_raw = _load(args.countable), _load(args.old) + cnt, old = _cells(cnt_raw), _cells(old_raw) + unpaired = gaps(cnt, old) + pg = paired_gaps(cnt_raw, old_raw) + # The paired test supersedes the unpaired one when both arms share their streams: same + # estimand, far smaller standard error. Keep the unpaired numbers for the variance- + # reduction report below. + g = unpaired if pg is None else unpaired.drop(columns=["gap", "se", "ci95", "t"]).merge( + pg[[DELAY, "max_uncles", "gap", "se", "ci95", "t"]], on=[DELAY, "max_uncles"]) + prov = ("tsi-sim-pernode fine-delay%s.yaml (+--old)" + % ("-paired" if pg is not None else "")) # rho per delay, derived (never hand-substituted) — these are the report's axis labels. delays = sorted(cnt[DELAY].unique()) @@ -210,11 +249,35 @@ def main() -> None: alle = float(np.sqrt(1.0 / w.sum())) print(f" whole band: {allp:+.5f} +-{Z95 * alle:.5f} t={abs(allp) / alle:.2f}") + if pg is not None: + print("\n=== PAIRED design (common random numbers) ===") + # Variance reduction actually achieved, per cell, vs the unpaired standard error. + cmp = unpaired[[DELAY, "max_uncles", "se"]].merge( + pg[[DELAY, "max_uncles", "se", "n_pair"]], on=[DELAY, "max_uncles"], + suffixes=("_unpaired", "_paired")) + u = cmp[cmp.max_uncles > 0] + ratio = (u.se_unpaired / u.se_paired.replace(0, np.nan)) + print(f" SE shrink at U>=1: median {ratio.median():.1f}x, range " + f"{ratio.min():.1f}-{ratio.max():.1f}x ({int(u.n_pair.min())} pairs/cell)") + pctl = pg[pg.max_uncles == 0] + exact, tot = int(pctl.n_zero.sum()), int(pctl.n_pair.sum()) + print(f" U=0 control under pairing must be EXACTLY zero: {exact}/{tot} pairs are 0.0" + f" -> {'PASSES' if exact == tot else 'FAILS — streams are not shared'}") + res = pg[(pg.max_uncles > 0) & (pg.t >= 2)] + print(f" per-cell resolved at |t|>=2: {len(res)}/{len(pg[pg.max_uncles>0])}" + f" (unpaired: {int((unpaired[unpaired.max_uncles>0].t>=2).sum())}/15)") + ctl = g[g.max_uncles == 0] if len(ctl): - print(f"\nU=0 negative control (true gap = 0): |gap| up to {ctl.gap.abs().max():.4f}, " - f"max t = {ctl.t.max():.2f}, 95% CI +-{ctl.ci95.max():.4f} " - f"-> control {'PASSES' if ctl.t.max() < 2 else 'FAILS'}") + # Under pairing the control gap is EXACTLY 0, so its se is 0 and t is 0/0. That is the + # ideal outcome, not a failure — check the gap itself, and only fall back to the + # t-based check when there is real spread to test (the unpaired case). + worst = float(ctl.gap.abs().max()) + exact = bool((ctl.se == 0).all()) if "se" in ctl else False + ok = (worst == 0.0) if exact else (float(ctl.t.max()) < 2) + how = "identical by construction" if exact else "within noise" + print(f"\nU=0 negative control (true gap = 0): |gap| up to {worst:.4g} ({how})" + f" -> control {'PASSES' if ok else 'FAILS'}") # Absolute test: does uncle recovery actually land on 1.0? Same question as the gap # test, asked without reference to the other model. diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py index 4f4951c..3a4bd92 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/config.py @@ -99,6 +99,19 @@ class SimConfig: # Old model only (--old): the uncle reference window w_u in slots, set directly. # Ignored by the countable model, which derives the window from window_absorption. uncle_window: int = constants.W_DEFAULT + # COMMON RANDOM NUMBERS for countable-vs-old comparisons. Off by default, and deliberately + # NOT part of key() — with it off every seed is byte-identical to before, so historical runs + # and --old bit-reproduction are untouched. + # + # The two uncle models normally draw independent streams (uncle_model is in the key), so a + # comparison pays the full between-run variance TWICE and the arms differ in stake draw, + # peering graph and every lottery outcome. With paired_streams=True the RNG root is derived + # from the model-independent part of the key instead, so both arms get the SAME stake, the + # SAME graph and the SAME lottery draws; the only difference is the uncle rule, and the + # per-replicate difference becomes a paired observation with the shared variance cancelled. + # Trajectories still diverge legitimately after epoch 0 — a different counted density feeds + # back into the next epoch's difficulty — which is the effect being measured, not noise. + paired_streams: bool = False max_uncles: int = 0 # U (0 = baseline, no uncles) uncle_strategy: UncleStrategy = "oldest" # Coin-flip inclusion prob for the "random" strategy. Only 0.5 reproduces the spec's @@ -319,16 +332,9 @@ class SimConfig: def period_T(self) -> int: return constants.period_T(self.k, self.f) - def key(self) -> tuple: - """Hashable identity used to seed the RNG deterministically. - - Must include EVERY field that affects the run (guarded by test_rng), otherwise two - distinct configs would share an RNG stream. ``uncle_model`` / - ``window_absorption`` are appended ONLY for the countable model: an ``--old`` run's - key is then byte-identical to the pre-redesign key, so ``--old`` bit-reproduces - historical runs (the two models still get distinct streams from the marker). - """ - base = ( + def _base_key(self) -> tuple: + """Identity fields shared by both uncle models — see ``key`` and ``seed_key``.""" + return ( self.n_nodes, self.stake_dist, self.pareto_shape, self.uniform_random, self.total_stake, self.latency, self.latency_stochastic, self.uncle_window, self.max_uncles, self.uncle_strategy, self.uncle_random_p, self.f, self.beta, @@ -345,9 +351,29 @@ class SimConfig: # NOTE: windowed_fork_choice and prune_arrival are deliberately excluded — they are pure # compute/memory optimisations that consume no RNG and (at jitter_mean == 0) change no # result, so pruned and full-matrix runs must share a seed (see test_pernode parity). + + def key(self) -> tuple: + """Hashable identity used to seed the RNG deterministically. + + Must include EVERY field that affects the run (guarded by test_rng), otherwise two + distinct configs would share an RNG stream. ``uncle_model`` / + ``window_absorption`` are appended ONLY for the countable model: an ``--old`` run's + key is then byte-identical to the pre-redesign key, so ``--old`` bit-reproduces + historical runs (the two models still get distinct streams from the marker). + """ if self.uncle_model == "old": - return base # historical (pre-uncle_model) key: --old bit-compat - return base + (self.uncle_model, self.window_absorption) + return self._base_key() # historical (pre-uncle_model) key: --old bit-compat + return self._base_key() + (self.uncle_model, self.window_absorption) + + def seed_key(self) -> tuple: + """The identity the RNG root is actually derived from (see ``rng.seedseq_for``). + + Identical to ``key`` except under ``paired_streams``, where it deliberately drops the + uncle-model marker so that a countable run and an ``--old`` run of the SAME cell draw + the SAME root seed — common random numbers, which is what makes the two arms a + *paired* sample (see ``paired_streams``). + """ + return self._base_key() if self.paired_streams else self.key() # Axes that can be swept; every SimConfig field is legal here. diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py index 79587f2..7a977f4 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/metrics.py @@ -15,6 +15,10 @@ _CONFIG_FIELDS = ( "link_latency_mean", "link_latency_dist", "blend_hops", "blend_delay_max", "init_dest", "init_spread", "uncle_model", "window_absorption", "uncle_window", "max_uncles", "uncle_strategy", + # Recorded so downstream analysis can TELL whether a countable/--old pair actually shared + # its RNG streams. The paired test is only valid on paired runs, and without this column + # the analysis silently falls back to the much weaker unpaired test. + "paired_streams", "f", "beta", "k", "genesis_d_factor", "epochs", "fixed_point", "legacy_block_count", "replicate", "adversary_frac", "adversary_strategy", "adversary_period", "adversary_withhold_epochs", diff --git a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/rng.py b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/rng.py index 96316da..b586b5c 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/rng.py +++ b/tools/simulators/tsi/tsi-sim-pernode/src/tsi_sim/rng.py @@ -17,7 +17,9 @@ from .config import SimConfig def _entropy(config: SimConfig) -> int: - payload = repr((config.root_seed, config.key())).encode() + # seed_key() == key() unless paired_streams is set, in which case the uncle-model marker is + # dropped so both arms of a comparison share one stream (common random numbers). + payload = repr((config.root_seed, config.seed_key())).encode() digest = hashlib.blake2b(payload, digest_size=16).digest() return int.from_bytes(digest, "big") diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py index 26e47fa..f868711 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_config.py @@ -140,8 +140,11 @@ def test_key_covers_every_field(): # uncle_window is read ONLY by the old model; under the (default) countable model it is # an ignored field, deliberately left in the base tuple at its old position so that an # --old run's key stays byte-identical to historical keys. + # paired_streams must NOT be in key(): it selects WHICH key the RNG root is derived from + # (see seed_key), so putting it in key() would perturb every historical seed and break + # --old bit-reproduction. Its own behaviour is pinned in test_rng.py. ignored = {"root_seed", "windowed_fork_choice", "prune_arrival", "early_stop", - "uncle_window"} + "uncle_window", "paired_streams"} names = {f.name for f in dataclasses.fields(SimConfig)} - ignored a = SimConfig() for name in names: @@ -152,6 +155,10 @@ def test_key_covers_every_field(): # ... and uncle_window IS distinguished under the old model, where it is live. old = SimConfig(uncle_model="old") assert old.key() != dataclasses.replace(old, uncle_window=old.uncle_window + 1).key() + # paired_streams leaves key() untouched but DOES change the seed derived from it. + a_paired = dataclasses.replace(a, paired_streams=True) + assert a.key() == a_paired.key() + assert a.seed_key() != a_paired.seed_key() def test_old_model_key_is_historical(): diff --git a/tools/simulators/tsi/tsi-sim-pernode/tests/test_rng.py b/tools/simulators/tsi/tsi-sim-pernode/tests/test_rng.py index 0c019c0..8f305fd 100644 --- a/tools/simulators/tsi/tsi-sim-pernode/tests/test_rng.py +++ b/tools/simulators/tsi/tsi-sim-pernode/tests/test_rng.py @@ -32,3 +32,77 @@ def test_replicates_differ(): b = run_trajectory(SimConfig(n_nodes=300, topology="regular", k=8, epochs=6, link_latency_mean=2.0, replicate=1)) assert a[-1]["mean_ratio"] != b[-1]["mean_ratio"] + + +def test_paired_streams_shares_the_root_across_uncle_models(): + """Common random numbers: with paired_streams the two arms draw the SAME root seed.""" + from tsi_sim.rng import seedseq_for + + kw = dict(n_nodes=50, max_uncles=2, blend_delay_max=5.0, topology="blend", + k=32, epochs=2, replicate=3, paired_streams=True) + c = SimConfig(uncle_model="countable", **kw) + o = SimConfig(uncle_model="old", **kw) + assert c.seed_key() == o.seed_key() # the marker is dropped + assert c.key() != o.key() # ...but identity still distinguishes them + assert seedseq_for(c).entropy == seedseq_for(o).entropy + + +def test_unpaired_is_the_default_and_separates_the_models(): + kw = dict(n_nodes=50, max_uncles=2, blend_delay_max=5.0, topology="blend", + k=32, epochs=2, replicate=3) + c, o = SimConfig(uncle_model="countable", **kw), SimConfig(uncle_model="old", **kw) + assert c.paired_streams is False and o.paired_streams is False + assert c.seed_key() == c.key() and o.seed_key() == o.key() + assert seedseq_for(c).entropy != seedseq_for(o).entropy + + +def test_paired_streams_does_not_perturb_unpaired_seeds(): + """The flag must not enter key(): every historical seed stays byte-identical. + + This is what protects --old bit-reproduction of the pre-redesign runs (report §9). + """ + from tsi_sim.rng import seedseq_for + + for model in ("countable", "old"): + base = SimConfig(uncle_model=model, n_nodes=50, max_uncles=2, k=32, epochs=2) + flagged = SimConfig(uncle_model=model, n_nodes=50, max_uncles=2, k=32, epochs=2, + paired_streams=False) + assert base.key() == flagged.key() + assert seedseq_for(base).entropy == seedseq_for(flagged).entropy + # and the old model's key is still exactly the base tuple (no marker appended) + o = SimConfig(uncle_model="old", n_nodes=50, k=32, epochs=2) + assert o.key() == o._base_key() + + +def test_paired_streams_gives_both_arms_the_same_stake_and_graph(): + """Pairing must reach the actual shared inputs, not just the root seed.""" + import numpy as np + + from tsi_sim import topology + from tsi_sim.rng import seedseq_for + from tsi_sim.stake import make_stake + + kw = dict(n_nodes=60, degree=4, topology="blend", max_uncles=2, k=32, epochs=2, + blend_delay_max=5.0, replicate=1) + c = SimConfig(uncle_model="countable", paired_streams=True, **kw) + o = SimConfig(uncle_model="old", paired_streams=True, **kw) + kids = {n: seedseq_for(cfg).spawn(cfg.epochs + 3) + for n, cfg in (("c", c), ("o", o))} + s_c = make_stake(c, np.random.default_rng(kids["c"][0])) + s_o = make_stake(o, np.random.default_rng(kids["o"][0])) + np.testing.assert_array_equal(s_c, s_o) # same stake draw + g_c = topology.build_path_latency(c, np.random.default_rng(kids["c"][1])) + g_o = topology.build_path_latency(o, np.random.default_rng(kids["o"][1])) + np.testing.assert_array_equal(g_c, g_o) # same peering graph + + +def test_paired_streams_is_recorded_in_the_output_row(): + """A paired run must be identifiable from its parquet alone. + + scripts/plot_fine_delay.py picks the paired test only when both arms report + paired_streams; if the flag were missing from the recorded config it would silently fall + back to the unpaired test and quietly discard the whole point of the paired sweep. + """ + from tsi_sim.metrics import _CONFIG_FIELDS + + assert "paired_streams" in _CONFIG_FIELDS From c8a23fd1df7394e24843c2a07d85334ea33f2dc1 Mon Sep 17 00:00:00 2001 From: Marcin Pawlowski Date: Wed, 5 Aug 2026 12:12:03 +0200 Subject: [PATCH 09/22] Report becomes the directory README; rebuild the contents block MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The report is now reports/tsi/README.md, so browsing to reports/tsi/ lands on the report itself rather than on an index that points at it. The old index carried nothing the report lacked except the note that report-figures/ holds the figures of record (the simulator folder does not commit its own), which is folded into §9; its section table is superseded by the report's own contents block. The "[Index]" self-link in the header is replaced by the simulator link the index used to carry. The contents block was inconsistent: §2 listed subsection titles, §3 and §6 listed bare numbers with no titles at all, and the appendices were crammed onto one line while their subsections went unlisted. Rebuilt from the document's actual headings so every entry has a real title, top-level entries carry a one-line gloss, and subsections sit indented under their parent. It now covers all 47 anchors, including B.1-B.4 and C.1-C.2 which were previously absent. scripts/build_html.py follows the rename (DOCS is a single document) and still renders clean: 47 anchors, 0 broken internal links, 0 unrewritten .md links, 37 images. Also adds configs/countable-vs-old-paired.yaml — the paired, 20-replicate version of the overload grid. §3.2a now rests on a paired design while §3.2 still rests on 5 unpaired replicates, which is why its U=1 cells at delta_max 16 and 32 sit unresolved at t ~ 0.5 against a replicate sd of 0.15. That sweep is running; the report is not yet updated from it. Co-Authored-By: Claude Opus 5 (1M context) --- reports/tsi/README.md | 974 +++++++++++++++++- reports/tsi/tsi-report.md | 944 ----------------- .../configs/countable-vs-old-paired.yaml | 36 + .../tsi/tsi-sim-pernode/scripts/build_html.py | 9 +- 4 files changed, 994 insertions(+), 969 deletions(-) delete mode 100644 reports/tsi/tsi-report.md create mode 100644 tools/simulators/tsi/tsi-sim-pernode/configs/countable-vs-old-paired.yaml diff --git a/reports/tsi/README.md b/reports/tsi/README.md index 2a29add..0d6908a 100644 --- a/reports/tsi/README.md +++ b/reports/tsi/README.md @@ -1,36 +1,968 @@ # Total-Stake-Inference parameter selection -*Per-node network simulation of Cryptarchia Total Stake Inference (TSI). Simulator: [`tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode). All runs at the true security parameter **k = 2160** unless noted; latency is in slots and **1 slot = 1 s**.* +*Per-node network simulation of Cryptarchia Total Stake Inference (TSI). Simulator: `tsi-sim-pernode`. All runs at the true security parameter **k = 2160** unless noted; latency is in slots and **1 slot = 1 s**.* -This report selects and justifies the TSI parameters for Cryptarchia from a per-node network simulation. The whole report is one document — **[tsi-report.md](tsi-report.md)** — and section numbers (§1–§9, Appendices A–C) are stable identifiers referenced from the simulator and from spec discussion. +*Section numbers (§1–§9, Appendices A–C) are stable identifiers — §3.2a and the appendix letters are cited from the simulator and from spec discussion, so they are preserved verbatim. Simulation code, configs and run data: [`tools/simulators/tsi/tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode).* -> **Uncle references.** The model analysed throughout is the **countable** one: counting-only references, deduplicated by slot, drawn from first-fork blocks only, within a window derived as `w_u = W_abs/f`. An **unrestricted** baseline — any orphan in the window at any fork depth — is measured alongside it for comparison. The two are indistinguishable in the design regime `ρ < 1` and diverge only under overload. See the model note at the top of the [report](tsi-report.md), the mechanism in [§2.1](tsi-report.md#s2-1), the comparison in [§3.2](tsi-report.md#s3-2)–[§3.2a](tsi-report.md#s3-2a), and the reproduction notes in [§9](tsi-report.md#s9). +--- ## Contents -**[Read the report →](tsi-report.md)** +**[1. Executive summary](#s1)** — the problem, what was found, and the recommended configuration. -| § | what it covers | +**[2. Model and method](#s2)** — what is simulated and how accuracy is measured. +  [2.1 The TSI algorithm — before and after uncle references](#s2-1) · [2.2 The equilibrium is bounded by 1](#s2-2) + +**[3. Findings](#s3)** — the evidence, in the order a designer needs it. +  [3.1 The per-node estimate is consensus-safe](#s3-1) +  [3.2 Latency biases TSI low; uncles recover it](#s3-2) · [3.2a The design band at high precision (`δ_max` 1–5)](#s3-2a) +  [3.3 When one uncle is not enough — the load `ρ`](#s3-3) · [3.4 The uncle window is set by block spacing](#s3-4) +  [3.5 The joint (W, U) region](#s3-5) · [3.6 Block rate `f` moves every threshold](#s3-6) · [3.7 Network size erodes the one-uncle margin](#s3-7) + +**[4. Design equations and parameter-selection algorithm](#s4)** — the sizing rules, calibrated, with worked examples. + +**[5. Discussion and caveats](#s5)** — the regime of validity and what is not covered. + +**[6. Robustness beyond the honest, deterministic regime](#s6)** — noise, attacks, and the incentive design. +  [6.1 Jitter](#s6-1) · [6.2 The load-feedback loop](#s6-2) · [6.3 Grinding by uncle suppression](#s6-3) · [6.4 Block withholding](#s6-4) +  [6.5 Withhold-then-rejoin grinding](#s6-5) · [6.6 Private-chain (selfish) withholding](#s6-6) +  [6.7 Block and uncle rewards](#s6-7) · [6.8 The soft inclusion rule](#s6-8) · [6.9 Multiple coalitions and bribery](#s6-9) +  [6.10 Fork rate and reorg depth](#s6-10) · [6.11 Organic stake churn](#s6-11) + +**[7. Parameter reference — what each knob does](#s7)** +  [7.1 Protocol parameters](#s7-1) · [7.2 Network / environment parameters](#s7-2) · [7.3 Model and attack knobs](#s7-3) + +**[8. Safest parameter selection and design](#s8)** — the recommendation and its rationale. +  [8.1 The selection](#s8-1) · [8.2 Design decisions and rationale](#s8-2) · [8.3 Residual risks and open items](#s8-3) +  [8.4 Capstone: the whole recipe in one run](#s8-4) · [8.5 Recommendation vs the current spec](#s8-5) + +**[9. Reproducibility](#s9)** — how to re-run every study. + +**Appendices** +  [A — the residual ~1 % offset: on-chain rounding of `f`](#sA) +  [B — the per-epoch sampling-noise floor](#sB): [B.1 mechanism](#sB-1) · [B.2 the ±0.9 % floor](#sB-2) · [B.3 delay makes it one-sided](#sB-3) · [B.4 what precision is meaningful](#sB-4) +  [C — consensus properties in detail](#sC): [C.1 per-epoch traces at scale](#sC-1) · [C.2 consensus rests on common initialization](#sC-2) + +--- + +> **The uncle-reference model analysed here.** Uncle references are *counting-only* — they never affect a block's validity ([§6.7](#s6-7)–[§6.8](#s6-8)) — and are deduplicated by **slot**, not by block ([§8.5](#s8-5)). The reference window is derived from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k`, which is the `W = 300 = 10/f` sizing rule of [§3.4](#s3-4). One structural constraint shapes the results: only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is the price of verifying every reference from chain data alone. This report calls that the **countable** model, and measures it against an **unrestricted** baseline in which any orphan in the window is referenceable at any fork depth ([§2.1](#s2-1), [§3.2](#s3-2), [§9](#s9)). The result: **in the design regime `ρ < 1` the two are practically identical.** A dedicated 40-replicate **paired** sweep of the operating band (`δ_max` 1–5, `ρ ≈ 0.21–0.41`), in which both arms share the stake draw, the peering graph and every lottery outcome so the uncle rule is the only difference, puts every `U ≥ 1` cell of both models in 0.998–1.001 and pins the first-fork cost at **nothing measurable up to `δ_max` = 3 and ~0.1 % at `δ_max` = 4–5** ([§3.2a](#s3-2a)). Differences appear only at `ρ ≥ 1`: the restriction trims ~1.4 % at `ρ ≈ 1`, and under overload (`ρ ≈ 1.8`) recovery saturates near 0.95 where the unrestricted model reaches ~1.00. Deep forks are unrecoverable by construction, so past `ρ ≈ 1` the ceiling is set by the fork *depth* profile and **no uncle cap buys it back** — a second, independent reason for the [§8](#s8) "keep `ρ < 1`" rule. The closed-form accuracy with the measured effective utilization, `log(1−f)/log(1−f/q_u)`, predicts every countable cell to within 0.2 %. + + +## 1. Executive summary + +**The problem.** A Cryptarchia node wins the right to produce a block through a stake-weighted lottery, and the lottery's difficulty must be tuned to the total stake that is actively online — a number nobody can read directly, because participants join, leave, and fail without notice. Total Stake Inference (TSI) is the protocol's answer: every node keeps its own estimate `D̂` of the active stake and continuously corrects it against the one thing it can observe — how often blocks actually appear on chain. + +**Why it matters.** If nodes disagree on the estimate, they disagree on who is allowed to produce blocks, and the chain can split. If the estimate is too low, the lottery becomes too easy — blocks come too fast, collide, and fork. And an attacker who could drag the estimate down would make the lottery cheaper for itself. So TSI must deliver three things at once: all nodes agree, the value is right, and nobody profits from bending it. This report tests all three by simulating every node individually — each with its own view of the network, its own estimate, and explicit message delays — at up to 32 000 nodes, with the network topology itself measured exactly up to one million nodes ([§3.7](#s3-7)). + +**What we found** + +1. **All nodes always agree.** In every run, at every network size and block rate tested (1 000–10 000 nodes at the production security parameter; to 32 000 in the size-scaling study, [§3.7](#s3-7); blocks every 10–30 s), all nodes computed *exactly* the same estimate — even though they constantly disagree about the newest blocks. The reason is structural: TSI measures a window buried deep in the finalized past, where every honest node sees identical history ([§3.1](#s3-1)). Two caveats keep this honest: agreement is not accuracy — nodes can unanimously agree on a wrong value (see next point) — and agreement is inherited from the common genesis value, not rebuilt: TSI maintains agreement but cannot repair a divergence that somehow arose ([Appendix C](#sC)). +2. **Network delay makes the estimate too low; uncle references fix it.** When blocks race, the losers ("orphans") drop off the chain and out of the count, so the network under-counts its own stake — by roughly a quarter to a third under Blend (the mix-network transport) delays, deepening with network size. The error is strictly one-sided: the equilibrium estimate is **bounded above by the true stake** — `D̂/D` cannot exceed 1 (no tested cell sits above 1 beyond sampling noise, which is why the accuracy plots are capped at 1; [§2.2](#s2-2)), so delay can only deflate the estimate, never inflate it. Letting each block also reference recent orphans ("uncles") puts them back into the count — counting *slots*, so a slot with two winners still counts once — and a single uncle reference per block restores the estimate to **exactly the true stake** (the recommended cap adds a one-uncle margin, [§8](#s8)) (the only residual is an optional ~1 % from on-chain rounding of the target rate, [§2.2](#s2-2)/[Appendix A](#sA)) ([§3.2](#s3-2)). +3. **Two sizing rules cover the deployments tested.** How many uncle slots a block needs (`U`) is dictated by the **load** — the number of blocks the whole network produces during the time one block needs to reach everyone (written `ρ`; formally `ρ = f·D_vis`, [§3.3](#s3-3)). The load counts the concurrent blocks each new block must be able to reference, and one uncle slot drains one of them per block — so `U` must be at least the load rounded up, plus one spare. How far back a block may reach for an orphan (`W`) is dictated by block spacing, not delay: about ten block intervals. The formal equations, their calibration, and worked examples are in [§4](#s4). +4. **Cheating doesn't pay.** Hiding blocks to deflate the estimate costs the attacker more than anyone else, heals within one epoch, and — for a full withdrawal — the lower estimate is simply the *correct* count of who is still participating ([§6.4](#s6-4)–[§6.5](#s6-5)). The one genuinely profitable attack is classic selfish mining, which needs roughly one-third of all stake and afflicts every Nakamoto-style chain, not TSI specifically; the damage it does to the estimate is repaired by the same uncle mechanism ([§6.6](#s6-6)). Rewarding uncles compensates the honest victims of delay and makes hiding strictly worse — but the reward must remain a bonus (a *soft* rule, never a validity requirement, which an attacker could turn into a tool for censoring or forking the chain), and the uncle + nephew rewards (the nephew reward pays the block that *includes* the reference) must together stay below one block reward, or deliberately orphaning one's own blocks becomes a business ([§6.7](#s6-7)–[§6.8](#s6-8)). +5. **Reorganisations stay shallow if the load stays low.** Forks are the cost centre: a deep reorg discards confirmed blocks. Fork depth grows with delay, and uncles keep it shallow (without them the deflated estimate over-produces blocks, and honest reorgs reach ~17 deep; with them, ~4). Against a private-chain attacker holding 10–30 % of stake trying to force the deepest reorg, keeping the load below one (few honest forks) keeps reorgs bounded and shallow (single digits to low tens of blocks even at 30 % stake) — but past that, at 30 % stake and heavy delay, fork-induced orphaning tips the attacker over an effective majority and reorgs become unbounded. The same "keep `ρ < 1`" rule that keeps the estimate accurate keeps reorgs shallow ([§6.10](#s6-10)). + +*Method note: results come from the per-node simulator at the production security parameter k = 2160, with the robustness and size-scaling studies at a reduced k = 256 where noted; the sizing rules are semi-empirical (their form follows from the fork/orphan mechanism, their constants are fitted to the sweeps) and are derived under honest, deterministic-delay conditions — noise, attacks, and incentives are treated in [§6](#s6).* + +**Recommended configuration** (Cryptarchia baseline f = 1/30, i.e. 30-second blocks; full rationale and residual risks in [§8](#s8)): + +| parameter | value | basis | +|---|---|---| +| security `k` | 2160 | [§3.1](#s3-1) | +| block rate `f` | 1/30 (30 s) | protocol; [§3.6](#s3-6) | +| uncle window `W` | **300 slots** (= 10 block intervals) | [§3.4](#s3-4), [§4](#s4) | +| uncle cap `U` | the **load rounded up, plus one** (`⌈ρ⌉ + 1`) under Blend; **1** suffices for plain direct gossip | [§3.3](#s3-3), [§4](#s4) | +| TSI learning rate `β` | **1** (one-epoch tracking) | [§6.5](#s6-5) | +| operating point | keep the **load below one** block per propagation delay, with margin | [§6.2](#s6-2), [§6.3](#s6-3) | +| peering degree | **4 is fine for smaller networks (up to N ≈ 2×10⁵); ≥ 6 beyond** — degree 4 exhausts U = 1 near N ≈ 8×10⁵ | [§3.7](#s3-7), [§8](#s8) | +| uncle rewards | **soft** inclusion (never validity); substantial `w_u` (the uncle *reward*; not the spec's `w_u`, which is the uncle *window* — this report writes that `W`) with **`w_u + w_n < 1`** | [§6.7](#s6-7)–[§6.8](#s6-8) | + +*"Load" (`ρ`) in this table is the quantity defined in finding 3 above: blocks produced network-wide per block-propagation delay, `ρ = f·D_vis` ([§3.3](#s3-3)). Keeping it below one means a single uncle slot per block can absorb every concurrent block; the `+1` in the uncle cap is the safety margin.* + +This report runs in section order: from this summary to the model and counting rule ([§2](#s2)); the evidence behind each finding ([§3](#s3)); the design equations and selection algorithm ([§4](#s4)–[§5](#s5)); robustness against noise, attacks and the incentive design ([§6](#s6)); the per-knob parameter reference ([§7](#s7)) and the safest selection with residual risks and spec deltas ([§8](#s8)); and reproducibility ([§9](#s9)) with the appendices — the residual ~1 % `f`-rounding offset ([A](#sA)), the ±0.9 % per-epoch noise floor ([B](#sB)), and consensus detail ([C](#sC)). + +--- + + +## 2. Model and method + +*In one sentence: we rebuild the network node by node — every block reaches every node late, along realistic message paths, and each node keeps its own chain and runs its own estimator — so if nodes could disagree, this simulation would show it.* + +Each of `N` nodes runs TSI on its **own** partial view. A global block tree is built under explicit message propagation: block `b` produced at slot `t` by node `p` becomes usable at node `j` after the propagation delay from `p` to `j`. Every node then computes its own canonical chain (the single chain it accepts as valid via the fork-choice rule; competing blocks become orphans), its own block density, and its own estimate `D̂`. The **primary model throughout this report is Blend** — the deployment target and the regime where the uncle parameters actually matter; direct gossip serves as the light-delay contrast: + +- **`blend`** (primary) — a random d-regular peering graph over which a block is first relayed through `hops` random nodes (the Blend cascade (Sphinx-style relays)), each adding a `Uniform(0, δ_max)` blending delay, before a final network-wide gossip. Each cascade leg is a shortest-path hop **over the shared gossip graph** — a random relay is reached *through the network*, not by a direct link — and the final gossip floods to every node from the **last** relay, so a block's visibility is re-centred on a random node each time; the relays are blind forwarders, so only the producer sees its own block early. The dominant delay is the per-hop blending `δ_max` (`blend_delay_max`), in **whole seconds** — this is where forks, and therefore the uncle cap `U` (uncle slots per block; [§3.3](#s3-3)) and the uncle window `W` (how far back a block may reference an orphan, in slots; [§3.4](#s3-4)), matter. +- **`regular`** (contrast, detail) — plain direct gossip over the same graph; a block reaches a node after the shortest weighted path (geographic per-link latency). Realistic links are **sub-slot** (~40–200 ms), so forks are rare and even `U = 0` nearly suffices — the delay-free limit against which blend is judged. + +Transport uses the **`geo`** distribution — a real-world geographic band mixture (short intra-region links, long inter-continental ones), the "natural" latency used throughout. The design laws of [§4](#s4) reach transport latency only through its *mean* — it enters solely via the mean path latency `ℓ_mean`, which feeds the mean visibility delay `D_vis = hops·δ_max/2 + (hops+1)·ℓ_mean` that the laws are actually written in ([§3.3](#s3-3)) — and this was tested directly: re-running the N = 1 000/4 000 grid with **exponentially distributed** links at the same mean leaves consensus untouched (spread 0, agreement 1.000) and every `U ≥ 1` cell identical within noise (≈ 0.99–1.01, means 1.001 exp vs 1.001 geo); only the *un-recovered* `U = 0` depth moves a few points (up to +0.09 shallower under exp, whose median link is shorter than its mean). Latency shape is a second-order effect confined to the regime the design avoids anyway. Both distributions draw each link **independently**, so this probes the latency *marginal*, not its spatial structure — geographically **correlated** latency (regional clustering that lets co-located nodes fork as a bloc) is not modelled; in the primary Blend regime the per-hop mixing delay dominates the geographic link term, so this is expected to remain second-order, but it is untested ([§8.3](#s8-3)). A third topology, **`full_mesh`** (single-hop, uniform latency), reproduces the reduced analytic model (the simplified companion model that collapses the network to one chain and one scalar estimate; [§5](#s5)) inside this engine and was used only for cross-validation — no figure in this report derives from it. + +**Who holds the stake.** Real stake is concentrated: a few large holders own most of it. We model this with a **Pareto** ("80/20") distribution — roughly 20 % of nodes hold 80 % of the stake — in every headline sweep, with equal-stake runs as a control. The exact split matters little to TSI, for a simple reason: the lottery hands a set of nodes wins in proportion to their *summed* stake, and TSI counts only the *total* number of blocks — so two different ways of splitting the same total stake produce statistically the same block density. Measured: consensus is identical under equal and Pareto stakes (spread 0, agreement 1.000 in both) and accuracy with uncles is indistinguishable. The equal-stake control (`runs/2026-07-24_090114_default`, N = 400, blend) has no cell-matched Pareto counterpart, so the *un-recovered* `U = 0` level is not compared across stake distributions here; the mechanism argument — concentrated stake means fewer *distinct* simultaneous winners, and a producer that wins twice does not fork with itself — remains untested at matched cells. Tail weight *was* tested at matched cells: re-running the N = 1 000/4 000 grid with a lighter Pareto tail (Lomax index 1.33 instead of 1.16) leaves consensus and every `U ≥ 1` cell unchanged within noise, and moves the *un-recovered* `U = 0` under-count by at most 0.025 (mean |Δ| = 0.012 over the four matched `U = 0` cells, 1.33 marginally *deeper*, each cell within ≈ 1.5 SEM) at k = 256 — less concentration means more *distinct* simultaneous winners, hence more forks to recover. The one place concentration could still matter is adversarial: a *whale* coalition's reward statistics are lumpier than a random coalition's, flagged as untested in [§6.5](#s6-5). + +**How we measure.** Every epoch, every node reports its own estimate. The first epochs of a run are a start-up transient — the estimate walking from its genesis guess to equilibrium — so we **discard the first half of every run ("50 % burn-in") and average over the remaining epochs**; each configuration is then repeated with several independent random seeds ("replicates") and averaged over those too. "Equilibrium" values in this report always mean that double average. *(The burn-in is a **measurement convention, not part of the protocol.** TSI itself just runs its recursion once per epoch, forever — each node's live estimate is simply the latest update, with no discarding or averaging. Burn-in is the standard steady-state-simulation technique of dropping the warm-up transient so a single reported number reflects the estimator's equilibrium, not its cold start; averaging the tail epochs and replicates additionally beats down the ±~0.9 % per-epoch sampling noise of [Appendix B](#sB) to the ±0.1–0.2 % standard errors quoted here. The 50 % cut is deliberately conservative — the estimator actually converges in ~2 epochs, [§3.2](#s3-2).)* Four quantities are tracked: + +- `D̂/D` — **accuracy**: the estimate divided by the true active stake. 1.0 = exact. With correct slot-counting ([§2.1](#s2-1)) and enough uncle slots the equilibrium is **1.0**; the only residual is an optional ~1 % from the on-chain integer rounding of `f` ([Appendix A](#sA)). +- `range_ratio` — **disagreement**: the highest minus the lowest node estimate, in `D̂/D` units. 0 means every node holds *exactly* the same value. +- `agreement_window` — **consensus on the measurement**: the fraction of nodes whose finalized measurement window contains exactly the same blocks — i.e., who count the same density. 1.0 = unanimous. +- `agreement_tip` — **consensus on the newest block**: the fraction of nodes currently sitting on the most common chain tip. This can be far below 1 while all of the above are perfect — nodes race over the newest blocks yet have long agreed on the finalized past ([§3.1](#s3-1)). + + +### 2.1 The TSI algorithm — before and after uncle references + +**The question.** What exactly does TSI compute, and what changed when uncle references were added to the protocol? + +**Why it matters.** Everything in this report — the under-count, the recovery, the parameter rules — follows from one design invariant and how the two protocol versions honour it; the report should be readable without the spec at hand. + +**The design invariant: one count per slot.** The slot lottery is calibrated so that *slots* activate at rate `f` — the probability a slot produces at least one block is `f`. Crucially a slot can have several winners (two nodes independently win the same slot), and the calibration counts such a slot **once**. TSI must count the same way, or a busy slot with two winners would read as more stake than a slot with one. So the quantity TSI infers stake from is the number of *occupied slots* in the window, not the number of blocks. + +**The algorithm.** Once per epoch each node measures the occupied-slot count `m` in the finalized window of `T` slots and nudges its estimate toward the target `f_p` (the block rate `f` as the on-chain integer rounding stores it): + +```python +m = occupied slots counted in the window (which slots count differs by version — below) +D̂_next = max(1, D̂ · (1 − β·(f_p − m/T)/f_p)) β = learning rate (deployed: 1) +``` + +Occupied slots more frequent than the target push the estimate up (the lottery then gets harder); less frequent pulls it down; `m/T = f_p` is the resting point. The two versions differ **only in which slots count**: + +- **Before uncle references (spec v1.0):** `m` counts only slots occupied by the *canonical* chain. Under Blend delay roughly a third of honest blocks are orphaned, so their slots vanish from `m`, the resting point sits far below truth (`D̂/D ≈ 0.64–0.74`, deepening with network size), and the deflated estimate makes the network *chronically over-produce* blocks at up to ~2× the target rate ([§3.2](#s3-2), fig1). Pre-uncle TSI is not viable under Blend. +- **With uncle references, counting whole blocks (the *unrestricted* model):** `m` also counts the *referenced uncles* — orphans pointed at from the canonical chain — which puts the delay-orphaned slots back into the count and lifts the resting point up toward `D`. Any orphan in the reference window is eligible regardless of how deep in a fork it sits, and references are deduplicated by *block identity*. This report analyses it as the comparison baseline throughout, and calls it the **unrestricted** model. +- **With uncle references, counting slots under the first-fork restriction (the *countable* model — the rules analysed here):** two changes. First, deduplication is by **slot**, not by block: a referenced uncle sharing a slot with a canonical block, or with another counted uncle, adds nothing. Second, only the **first block of a fork** — one whose parent lies on the referencing chain — is countable, which is what makes every reference verifiable from chain data alone (deeper fork blocks would need the fork branch's ledger state). References never affect a block's validity; they are *counting-only*, the soft-rule property the incentive analysis requires ([§6.7](#s6-7)–[§6.8](#s6-8)). The reference window is *derived* from a **window absorption parameter**, `w_u = W_abs/f` with `W_abs = 10` expected block-intervals and bound `W_abs ≤ 0.6·k` — the `W = 10/f` sizing rule of [§3.4](#s3-4). The price of chain-only verifiability is that deep-fork orphans are unrecoverable by construction; [§3.2](#s3-2) measures what that costs, and the answer is nothing in the design regime and a bounded ceiling under overload. + +Slot deduplication is what makes the recovered equilibrium exactly 1.0 rather than a ceiling above it. Counting uncle *blocks* instead double-counts same-slot co-winners (one canonical, one referenced orphan) and inflates the equilibrium by the fixed multi-winner factor `c(f) ≈ 1.017` — a genuine accuracy bias, not a simulation artefact. Every result in this report uses the slot count; where a figure or table compares the two referencing models, the unrestricted baseline is labelled as such ([§9](#s9)). + + +### 2.2 The equilibrium is bounded by 1 + +**The question.** Slot-counting settles the resting point at `D` ([§2.1](#s2-1)). Can the estimate sit *above* the true stake — and does the epoch-to-epoch jitter around the resting point cost nodes winning probability? + +**Why it matters.** The estimate is the lottery's divisor: each node's per-slot win chance is `φ = 1 − (1−f)^(w_i/D̂)` (`w_i` = the node's stake). Whatever moves `D̂` moves every node's chance of winning slots — and with it block rewards and the pace of the chain. + +**It cannot exceed the true stake.** TSI counts *occupied slots*, and a window can hold no more occupied slots than actually occurred, so the counted density is capped at the true rate `f` and the equilibrium `D̂/D` is **bounded by 1** — it recovers *up to* exactly 1 (full uncle recovery) and sits below it when delay orphans slots faster than uncles restore them ([§3.2](#s3-2)). The old `c(f) ≈ 1.017` ceiling above 1 was an artefact of counting uncle *blocks*; slot-counting removes it ([§2.1](#s2-1), [Appendix A](#sA)). Around that bounded equilibrium each epoch's finite-window measurement carries ≈ ±0.9 % sampling noise (`√((1−f)/(f·T))` at k = 2160), which averages out over the burn-in ([Appendix B](#sB)) and is *fairness-neutral* — all nodes share the same `D̂`, so relative win rates are untouched; only the block pace breathes by ±0.9 % epoch to epoch, with no systematic bias. + +**The one residual bias is the on-chain rounding of `f`, and it is optional.** The spec stores the target as a three-decimal on-chain integer, `f_p = 0.033` rather than `1/30`, and driving the density to `f_p` leaves the estimate high by the fixed factor `f/f_p ≈ 1.010`. It is common to every node, so fairness is untouched; it is removed by carrying `f` at higher precision, and **this report's estimator drives the density to exact `f`, so every result here is unbiased**. This is the *only* systematic offset from 1 that the counting fix leaves — and the sole reason a deployed `D̂/D` would read ≈ 1.01 rather than 1.00. [Appendix A](#sA) derives it and sizes the one-constant spec change that removes it ([§8](#s8) row 14). + +--- + + + +## 3. Findings + +Seven findings, in the order a designer needs them: nodes agree ([§3.1](#s3-1)); delay biases the estimate low and uncles fix it ([§3.2](#s3-2)); when one uncle is not enough ([§3.3](#s3-3)); how wide the reference window must be ([§3.4](#s3-4)); how the two levers combine ([§3.5](#s3-5)); what changes with the block rate ([§3.6](#s3-6)); and how network size erodes the one-uncle margin ([§3.7](#s3-7)). Each finding is stated first; the tables and figures carry the evidence. + + +### 3.1 The per-node estimate is consensus-safe — with and without uncles + +**The question.** Do all nodes compute the *same* estimate — including when blocks carry uncle references? + +**Why it matters.** If nodes disagreed on `D̂` (the per-node estimate of the active stake), they would disagree on who is allowed to produce blocks — a consensus split; and the uncle mechanism this report recommends must not be able to cause one. This is the precondition every later finding stands on, which is why it comes first. + +**Result: agreement is exact, at every uncle cap tested (`U` = 0…3).** At the full security parameter k = 2160, the highest and lowest node estimates are identical (spread exactly 0) and **window agreement** — the fraction of nodes that count *exactly the same finalized blocks* in their measurement window — is 1.000, across all network sizes, block rates (10–30 s), and uncle caps: + +| N | 1 000 | 2 000 | 5 000 | 10 000 | +|---|---|---|---|---| +| `range_ratio` (spread of `D̂/D`) | 0 | 0 | 0 | 0 | +| `agreement_window` | 1.000 | 1.000 | 1.000 | 1.000 | + +Nodes *do* disagree about the newest blocks (tip agreement dips to ~0.96 in the worst cell) — but TSI never reads the newest blocks: it measures a window buried far past k-finality (blocks deeper than `k` are final — no honest node ever reorganises them), where all honest nodes provably hold identical history, uncle references included. **Consequence:** TSI can be treated as one global estimate, adding uncle references (and paying rewards for them) does not endanger that, and the rest of this report may speak of "the" estimate in the singular. Per-epoch traces at N = 10 000, the tip-agreement detail, and why an injected disagreement would *not* heal itself are in **[Appendix C](#sC)**. + + +### 3.2 Latency biases TSI low; uncles recover it to exactly 1 + +**The question.** How accurate is the agreed-upon estimate — and do uncle references actually earn their place in the protocol? + +**Why it matters.** An estimate that is too low makes the lottery too easy — blocks come faster than the target, collide more, and the safety margin erodes; this section measures how much accuracy is lost to network delay and how much of it uncles buy back. + +**The mechanism in one line.** When two blocks race, the loser (an "orphan") drops off the chain — and out of the block count that TSI reads — so the network systematically under-counts its own stake; an **uncle reference** lets a later block point at a recent orphan and put it back into the count. + +**Result: without uncles the estimate is 26–37 % low; one uncle recovers it fully.** Full-scale measurement under Blend (`D̂/D` = accuracy, the estimate over the true stake; each entry the mean over all sweep cells — every degree × link-latency × blending-delay combination, 6–20 replicates, equilibrium protocol of [§2](#s2); the N = 1 000/2 000 and N = 5 000/10 000 rows are pooled from two sweeps run on *different* grids — link-latency {0.1–1.0} slots × U ≤ 3 for the smaller sizes, {0.5} slot × U ≤ 2 for the larger — so the four rows are not measured on a single common grid, though the monotone deepening also holds on the matched 0.5-slot subgrid, 0.721/0.688/0.650/0.635): + +| N | `D̂/D`, U = 0 | `D̂/D`, U ≥ 1 | +|---|---|---| +| 1 000 | 0.739 | 1.000 | +| 2 000 | 0.722 | 1.000 | +| 5 000 | 0.650 | 0.999 | +| 10 000 | 0.635 | 1.000 | + +The U = 0 under-count **deepens with N** (more nodes → more concurrent proposals → more orphans). One uncle restores accuracy to **exactly 1** at every size *in this sweep* (`fig2`) — because its delay grid keeps the load `ρ` (blocks produced per propagation delay, [§3.3](#s3-3)) below one; [§3.7](#s3-7) shows that at much larger N, sparse peering pushes `ρ` past what one uncle can drain, and U = 1 stops sufficing. + +**Why exactly 1 (and not a ceiling above it):** because TSI counts *occupied slots*, not blocks ([§2.1](#s2-1)). The lottery activates slots at rate `f`; uncles put the delay-orphaned slots back into the count, one per slot, and never double-count a slot that already has a canonical block — so holding the counted slot density at `f` settles the estimate at `D`. Verified in isolation at zero network delay, where the only orphans are same-slot co-winners: the committed `U = 0` series (full mesh, `L = 0`, `runs/fluctuation_u0.parquet`, [Appendix B.2](#sB-2)) sits at `D̂/D = 0.9997 ± 0.0085` (k = 2160, per-epoch σ over 4 × 120 epochs), and a matching `U = 2` arm at the same settings lands at `1.000` — the co-winner slots are counted once, not twice, so no ceiling appears (the `U = 2` arm was run ad hoc and is not committed; recipe in [§9](#s9)). (The remaining ~1 % offset the deployed estimator carries comes only from the on-chain integer rounding of `f`, [§2.2](#s2-2) / [Appendix A](#sA).) + +![Fig 2 — per-node D̂/D vs uncle cap U (curves: max blending delay per hop = 1/2/3 slots, averaged over N): without uncles the estimate is biased low — deeper as blending delay grows — and one uncle restores it to exactly 1.](report-figures/fig2_uncle_recovery.png) + +**What the first-fork restriction costs.** Running the delay × U grid under both referencing models on the same grid (`configs/countable-vs-old.yaml`, N = 1 000, blend, 3 hops, 5 replicates; [§9](#s9)) separates the regimes cleanly (`fig30`). Cells are replicate means ± SEM; `t` is the two-sample statistic for the countable−unrestricted gap, and cells with `t < 2` do **not** resolve a difference at this replicate count: + +| `δ_max` (s) | ρ | U | countable | unrestricted | gap (t) | +|---|---|---|---|---|---| +| 4 | ≈ 0.36 | 1 / 2 / 4 | 0.9979 ± 0.0015 / 0.9982 ± 0.0014 / 0.9995 ± 0.0012 | 0.9981 ± 0.0006 / 0.9985 ± 0.0012 / 0.9992 ± 0.0013 | *none resolved* (0.1–0.2) | +| 8 | ≈ 0.56 | 1 / 2 / 4 | 0.9965 ± 0.0015 / 0.9955 ± 0.0017 / 0.9963 ± 0.0015 | 0.9986 ± 0.0017 / 0.9993 ± 0.0016 / 0.9989 ± 0.0017 | *none resolved* (1.0–1.6) | +| 16 | ≈ 0.96 | 1 | 0.9647 ± 0.0065 | 0.9610 ± 0.0043 | *not resolved* (0.5) | +| 16 | ≈ 0.96 | 2 / 4 | 0.9862 ± 0.0010 / 0.9911 ± 0.0032 | 0.9999 ± 0.0005 / 1.0013 ± 0.0011 | −0.014 (12.1) / −0.010 (3.0) | +| 32 | ≈ 1.76 | 1 | 0.608 ± 0.069 | 0.570 ± 0.042 | *not resolved* (0.5) | +| 32 | ≈ 1.76 | 2 / 4 | 0.9343 ± 0.0015 / 0.9517 ± 0.0007 | 0.9774 ± 0.0064 / 1.0020 ± 0.0010 | −0.043 (6.5) / −0.050 (41.0) | + +**The `U = 0` rows are a negative control.** With no uncles the two models are identical by construction — no reference is ever taken, so any measured gap is pure between-run noise (the two models draw independent RNG streams by design, so the comparison is unpaired). That control reads **+0.010 (t = 0.8) at `δ_max = 4`** but **−0.230 (t = 2.1) at `δ_max = 32`**, where single replicates range from 0.05 to 0.60. Read the table against that floor: at `δ_max = 32` a gap must clear ~0.2 to mean anything on a single-replicate basis, which is exactly why the `U = 1` cells there are reported as unresolved while the tightly-clustered `U = 2` and `U = 4` cells are not. + +So: **at the operating loads (`ρ < 1`) no difference between the models is detectable at all** — the first-fork restriction costs nothing measurable where forks are shallow, and both models sit at ≥ 0.995 for every `U ≥ 1`. ([§3.2a](#s3-2a) puts a much tighter bound on this region.) Differences appear only at `ρ ≥ 1` and only at `U ≥ 2`: at `ρ ≈ 1` the restriction trims ~1.4 %, and in overload the countable recovery **saturates** — raising `U` 2 → 4 buys only 0.934 → 0.952 while the unrestricted model reaches ~1.00. The ceiling is the measured recovery rate `r` (0.92 at `δ_max = 32`, `U = 4`), set by the fork-*depth* profile rather than by capacity, so no uncle cap buys it back. The closed form `D̂/D = log(1−f)/log(1−f/q_u)` with the measured `q_u = q + (1−q)·r` predicts every countable cell to within 0.2 % (`fig31`). + +`fig32` shows `r` and the residual `1−r` per delay, rising from 0.3 % to 7.8 % of the waste as `δ_max` goes 4 → 32 at `U = 4`. That residual is the *combined* first-fork and capacity loss — the simulator cannot separate the two, because the restriction acts at selection (a deep orphan is simply never referenced) rather than at counting. At `U = 4`, where capacity is not binding for `ρ ≤ 1.8`, most of it is attributable to fork depth; the split is not measured directly. + +![Fig 30 — equilibrium D̂/D vs Blend mixing delay, countable (solid) vs unrestricted (dashed) per uncle cap, error bars = replicate SEM. The U=0 pair is the negative control: the models are identical with no uncles, so the visible gap there — small at low delay, large at 32 — is the pure between-run noise floor. Countable saturates below 1 in overload, where deep forks are unrecoverable by construction.](report-figures/fig30_countable_vs_old.png) + +![Fig 31 — the q→q_u reduction check: predicted log(1−f)/log(1−f/q̄_u) from the measured q̄_u vs the simulated equilibrium, all countable U≥1 cells on the diagonal within 0.2 %.](report-figures/fig31_countable_prediction.png) + +![Fig 32 — measured recovery rate r (left) and the non-recovered waste share 1−r on a log axis (right) vs mixing delay: near-total recovery at design loads; the residual — first-fork and capacity losses combined, which this measurement cannot separate — grows with delay.](report-figures/fig32_countable_recovery.png) + +**Bootstrap is self-limiting — but only with uncles** (`fig1`; full scale, k = 2160, Blend, N = 1 000 and 5 000, genesis guesses 0.01×–2× the true stake; 0.1×–2× at N = 5 000). With uncles (U = 2, solid lines) the cold start is a non-event: whatever the guess, block production snaps back to the target `f` within ~2–2.5 epochs and the estimate lands on 1.0 by epoch 2 — identically at both network sizes. Without uncles (U = 0, dashed) the system also converges from any guess, **but to the wrong place**: the estimate settles below truth (mean ≈ 0.58× across guesses, ranging ≈0.48–0.85; ≈0.51× at N = 5 000) and the network then *chronically over-produces* blocks at ~1.85× the target rate (~2.0× at N = 5 000) — the [§6.2](#s6-2) load feedback in the flesh (a low estimate makes the lottery easier, extra blocks orphan, the count stays low). So uncle references are load-bearing from the very first epochs: they are what makes the bootstrap end *at the truth* rather than at a permanently overheated equilibrium. + +![Fig 1 — bootstrap at full scale (k=2160, Blend, N=1000): from any genesis guess (0.01×–2×), with uncles (solid, U=2) block production (top) and the estimate (bottom) converge to the target f and D̂/D = 1.0 within ~2–3 epochs (≈2 from a near-correct guess, ~3 from the extreme 0.01× start); without uncles (dashed, U=0) they settle more slowly to a chronically overheated, guess-dependent equilibrium — D̂/D ≈ 0.48–0.85 (mean ≈ 0.58; ≈ 0.51 at N=5000), block rate ≈ 1.2–2.1×f.](report-figures/fig1_bootstrap.png) + + +### 3.2a The design band at high precision — `δ_max` 1–5 + +**The question.** [§3.2](#s3-2) samples the mixing delay at 4/8/16/32 with five replicates. That resolves the overload regime, but it leaves the band the parameters are actually chosen in measured at four-fold spacing and low power — enough to say "no difference detected" and nothing more. How accurate is TSI across `δ_max` = 1–5, and how large a first-fork cost can be *excluded* there? + +**The finding.** One uncle slot holds the estimate at the true stake across the whole band: every `U ≥ 1` cell under both referencing models lands in **0.998–1.001**, flat in delay, while the uncle-free baseline decays 0.806 → 0.623. The first-fork restriction costs **nothing measurable up to `δ_max` = 3** and about **0.1 %** at `δ_max` = 4–5. + +**The design is paired.** The two referencing models normally draw independent RNG streams — `uncle_model` is part of the config key, which is what lets `--old` bit-reproduce earlier runs ([§9](#s9)) — so a comparison pays the between-run variance twice and the arms differ in stake draw, peering graph and every lottery outcome. `configs/fine-delay-paired.yaml` sets `paired_streams`, which derives the RNG root from the model-independent part of the key: both arms then get the **same stake, the same graph and the same lottery draws**, and the uncle rule is the only difference. Each replicate becomes a matched pair, the shared variance cancels, and the test is a one-sample t on the 40 per-replicate differences. Trajectories still diverge after epoch 0 through the genuine feedback — a different counted density changes the next epoch's difficulty — which is the effect being measured, not noise. Grid: `δ_max` ∈ {1,2,3,4,5}, `U` ∈ {0,1,2,4}, 40 replicates, N = 1 000, blend, 3 hops, spanning `ρ ≈ 0.21` to `0.41`. + +| `δ_max` (s) | ρ | `U=0` (both models) | `U≥1` countable | `U≥1` unrestricted | pooled gap (t) | +|---|---|---|---|---|---| +| 1 | ≈ 0.21 | 0.806 | 0.9995 – 1.0004 | 0.9990 – 1.0010 | −0.0003 ± 0.0005 (1.1) | +| 2 | ≈ 0.26 | 0.763 | 0.9993 – 0.9996 | 0.9996 – 1.0003 | −0.0004 ± 0.0005 (1.8) | +| 3 | ≈ 0.31 | 0.723 | 0.9993 – 0.9997 | 0.9992 – 1.0004 | −0.0003 ± 0.0004 (1.4) | +| 4 | ≈ 0.36 | 0.668 | 0.9982 – 0.9997 | 0.9995 – 0.9999 | **−0.0011 ± 0.0004 (4.7)** | +| 5 | ≈ 0.41 | 0.623 | 0.9986 – 0.9992 | 0.9995 – 1.0003 | **−0.0009 ± 0.0005 (3.7)** | + +**The negative control is now an identity check.** With `U = 0` no reference is ever taken, so under shared streams the two arms must produce *bit-identical* trajectories — not merely agree within noise. They do: **all 200 replicate pairs differ by exactly 0.0**, at every delay. That is a far stronger validation than the unpaired design could offer, where the same control only had to agree within a ±0.025 band and in fact drifted by 0.016. + +**What pairing bought.** Per-cell standard errors shrink by a median factor of 1.6 (range 1.2–2.1), taking the widest 95 % CI from ±0.0015 to **±0.0010**. Five of the fifteen `U ≥ 1` cells now resolve at |t| ≥ 2 against 0.75 expected by chance, and the largest (`U = 2`, `δ_max = 4`, t = 4.32) clears the Bonferroni threshold of 2.94 for 15 tests. The unpaired sweep resolved only `δ_max = 5`, and only after pooling. + +**The cost is a step, not a ramp.** Pooling across the three uncle caps — separate draws of the same underlying difference — `δ_max` 1–3 stay unresolved (t = 1.1, 1.8, 1.4) and then **`δ_max` = 4 and 5 both resolve**, at −0.0011 (t = 4.7) and −0.0009 (t = 3.7). Over the whole band the pooled gap is −0.00060 ± 0.00021, **t = 5.7** — comfortably resolved, where the unpaired estimate of the same quantity (t = 2.8) did not survive correction. So the restriction switches on somewhere around `δ_max` ≈ 4 rather than growing smoothly with delay, and above that it sits near 0.1 % without deepening across the band tested. Measured against the exact target 1.0 instead of against the other arm — a more sensitive view of the same countable data, not independent evidence — the same picture appears: the unrestricted model has 1 of 15 cells below 1 (chance), the countable model has 5, all at `δ_max` 4–5. + +**How big is 0.1 %.** An order of magnitude below the ±0.9 % per-epoch sampling noise of [Appendix B](#sB), and below the ~1 % fixed-point rounding bias of [Appendix A](#sA). The [§1](#s1) statement that one uncle restores the estimate to the true stake holds at the precision that matters; this section puts the residual at ~0.1 % at the top of the band rather than at zero. + +![Fig 34 — design-regime accuracy, δ_max 1–5, countable (solid) vs unrestricted (dashed) per uncle cap under common random numbers, error bars = replicate SEM over 40 pairs: every U ≥ 1 curve sits at 1.000 across the band under both models (to within 0.2 %), while U = 0 — the negative control — decays 0.81 → 0.62 identically for both.](report-figures/fig34_fine_delay_accuracy.png) + +![Fig 35 — the paired countable − unrestricted gap with 95% CIs, with the inverse-variance pooled estimate in black: flat and unresolved through δ_max = 3, then a resolved ~0.1 % cost at δ_max = 4 and 5.](report-figures/fig35_fine_delay_gap.png) + +**What this settles.** One uncle slot is sufficient everywhere in the operating band under either referencing model — the [§3.3](#s3-3) `U ≥ ⌈ρ⌉` rule has margin to spare at `ρ ≤ 0.41`, and raising `U` past 1 does not remove the residual (all three caps show the same ~0.1 % shortfall at `δ_max` = 4–5, so it is not a capacity limit). And the first-fork restriction, which [§3.2](#s3-2) shows costing 1.4 % at `ρ ≈ 1` and 5 % under overload, costs **about 0.1 %** at the top of the design band and nothing measurable below it. + + +### 3.3 One uncle is not always enough — the load `ρ` + +**The question.** [§3.2](#s3-2) showed a single uncle slot sufficing across its delay grid. When does that stop — how much delay can one uncle slot actually handle? + +**Why it matters.** Blend's per-hop blending delay is a privacy knob that may be turned up after deployment; the protocol needs to know at which point every extra second of delay demands another uncle slot. + +**The intuition.** One uncle slot per block can absorb one orphan per block — so it keeps up only while the network creates orphans no faster than that. The deciding number is the **load** `ρ`: how many blocks the whole network produces during the time one block needs to become visible everywhere. The symbols used below, in one place: + +| symbol | meaning | |---|---| -| [§1](tsi-report.md#s1) | executive summary — the problem, the findings, the recommendation | -| [§2](tsi-report.md#s2) | the model, the measurement convention, and the counting rule | -| [§3](tsi-report.md#s3) | the findings and their evidence, including the high-precision design band ([§3.2a](tsi-report.md#s3-2a)) | -| [§4](tsi-report.md#s4) | design equations and the parameter-selection algorithm | -| [§5](tsi-report.md#s5) | caveats and regime of validity | -| [§6](tsi-report.md#s6) | robustness — jitter, grinding, withholding, selfish mining, rewards, reorg depth, churn | -| [§7](tsi-report.md#s7) | parameter reference — what each knob does | -| [§8](tsi-report.md#s8) | the safest selection, residual risks, and the recommendation-vs-spec deltas | -| [§9](tsi-report.md#s9) | reproducibility — how to re-run every study | -| [A](tsi-report.md#sA) · [B](tsi-report.md#sB) · [C](tsi-report.md#sC) | the residual `f`-rounding offset · the per-epoch noise floor · consensus detail | +| `f` | block rate (blocks per slot; `1/30` = one block every 30 s) | +| `ℓ_mean` | mean gossip path latency between two nodes (slots) | +| `hops`, `δ_max` | Blend cascade length and the per-hop blending-delay bound (mean per-hop delay = `δ_max/2`) | +| `D_vis` | mean **visibility delay** = `hops·δ_max/2 + (hops+1)·ℓ_mean` under Blend (plain gossip: just `ℓ_mean`) | +| **`ρ`** | **load** = `f·D_vis` — blocks produced per visibility delay = orphans each canonical block must absorb | +| **`U`** | **uncle cap** = uncle slots per block ([§3.3](#s3-3)) | +| **`W`** | **uncle window** = how far back a block may reference an orphan, in slots ([§3.4](#s3-4)); distinct from `T`, the measurement window of [§2.1](#s2-1) | -## Headline recommendation +**Result: one uncle works up to `ρ ≈ 1`, and nothing else stretches that.** Accuracy at U = 1, plotted against `ρ` for **every** block rate and delay tested, collapses onto a single curve that breaks at `ρ ≈ 1` (`fig6`, right): **U = 1 recovers iff `ρ ≲ 1`.** Two bounds govern the cap: `U < ρ` **never** recovers (orphans arrive faster than they can be referenced; the queue grows without bound and no window helps) — a hard necessary condition; and empirically `U ≈ ⌈ρ⌉` (the load rounded up) *suffices*, with a one-uncle margin needed near integer `ρ` because the true concurrency window is about `2·D_vis`, not `D_vis` (the factor a ≈ 2 in eq. 4′, [§4](#s4)). -Cryptarchia baseline f = 1/30. Two design choices are foundational: count uncles **per occupied slot**, not per block — the density-bug fix that lands the estimate at exactly `D` ([§2.1](tsi-report.md#s2-1), [§8.5](tsi-report.md#s8-5)) — and make genesis `D̂` **a single protocol constant, identical at every node**, never client-configurable, since a per-node divergence is never self-corrected ([§8.1](tsi-report.md#s8-1) row 7). The settings: security `k = 2160`, uncle window `W = 300` slots, uncle cap `U ≥ ⌈ρ⌉ + 1` (2 at the Blend target; the protocol's `MAX_UNCLES = 4` sits safely above it), learning rate `β = 1`, on-chain `f` at 10⁻⁶ precision, peering degree ≥ 6 at scale, soft uncle rewards with `w_u + w_n < 1`, and operate at load `ρ = f·D_vis < 1`. The full recommended-configuration table and rationale are in **[§8 →](tsi-report.md#s8)**. +Sweeping the delay directly (`fig16`) makes the law visible: accuracy sits at 1.0 until the load crosses the uncle cap, then falls off — `U = 0` collapses immediately, `U = 1` holds to `ρ ≈ 1` (`D_vis ≈ 30` s), `U = 2` to `ρ ≈ 2` (`≈ 60` s), and `U = 3` across the whole tested range. -## Figures +![Fig 16 — recovered relative stake D̂/D vs mean visibility delay D_vis (Blend, f=1/30; N = 800, degree 8, uniform stake, 5 replicates at a reduced k = 48 so the delay axis could be swept densely): each uncle cap U holds accuracy at 1.0 until ρ=f·D_vis exceeds U, marked at ρ=1, 2. The reduced k widens the per-epoch sampling noise, so a few U ≥ 1 points sit fractionally above the 1.0 line (largest 1.016 ± 0.011 at D_vis ≈ 14 s, < 2 SEM) — the ≤ 1 bound itself is resolved at k = 256 with 20 replicates in `fig26` below.](report-figures/fig16_stake_vs_delay.png) -Figures are embedded from [`report-figures/`](report-figures) via relative links and are versioned here alongside the report. They are produced by the simulator's plotting scripts (`scripts/*.py` and `tsi_sim.plotting`) in [`tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode); that simulation folder does **not** commit its own generated figures — the copies checked in here are the report's figures of record. +![Fig 3 — recovery (mean D̂/D) over hops × per-hop blending budget for uncle caps U ∈ {0,1,2,4}: one uncle recovers only while the total delay stays small, and raising the cap restores it. The axes show the per-hop budget; the total mean visibility delay D_vis runs from ≈11 s (3 hops, δ_max=4) to ≈104 s (6 hops, δ_max=32).](report-figures/fig3_hops_delay.png) -## Reproducing the results +The full sweep behind `fig3` spans hops 3–6 × per-hop budget 4–32 s × `U ∈ {0, 1, 2, 4}` at both N = 1 000 and N = 2 000. Note the axes show the *per-hop* budget — the total mean delay is what matters, e.g. 3 hops at `δ_max = 8` mean 3·4 = 12 s of blending plus ≈ 5 s of gossip → `D_vis ≈ 17` s (`ρ ≈ 0.56`), while 6 hops at `δ_max = 32` reach `D_vis ≈ 104` s (`ρ ≈ 3.5`). More hops at a fixed budget raise `D_vis` and degrade U = 1 exactly as the load predicts (at `δ_max = 16`: accuracy 0.96 at 3 hops → 0.52 at 6 hops), and raising the cap restores it up to the longest cascade — U = 2 clears the `0.98` recovery bar ([§3.6](#s3-6)) in every `δ_max ≤ 8` cell (≥ 0.998) and at `δ_max = 16` through 5 hops, but **not at 6 hops**: `1.000 ± 0.001` (3 hops) → `0.962 ± 0.007` (6 hops), a 2.6σ shortfall, and `0.941 ± 0.004` (11σ) at N = 2 000; the hops-average is 0.986. That cell carries `ρ ≈ 1.8` — exactly the load at which [§3.6](#s3-6) finds U = 2 genuinely insufficient. `δ_max = 32` needs U = 4 (hops-averaged 0.983, vs 0.755 at U = 2), and even U = 4 falls to `0.945 ± 0.004` at 6 hops — consistent with `⌈ρ⌉` rising to ~2–4 across the hops axis (U = 3 was not swept). The N = 2 000 half reproduces the same pattern (hops-averaged U = 2: 0.981 at `δ_max ≤ 16`; U = 4: 0.981 at 32, with the same 6-hop shortfalls). -The simulation code, configs, and run data live in [`tools/simulators/tsi/tsi-sim-pernode`](../../tools/simulators/tsi/tsi-sim-pernode). Every study's exact command is listed in [§9 — Reproducibility](tsi-report.md#s9). In short, from the simulator directory: `make install`, then `make ` to run a sweep (results land under `runs/_

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