15e876e90a
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) <noreply@anthropic.com>
Total-Stake-Inference parameter selection
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. 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 regimeρ < 1and diverge only under overload. See the model note at the top of Part 1, the mechanism in §2.1, the comparison in §3.2–§3.2a, and the reproduction notes in §9.
Parts
- Overview and recommendations — the executive summary, the per-knob parameter reference (§7), and the safest selection with residual risks and the recommendation-vs-spec deltas (§8).
- Accuracy and design — 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).
- Robustness and incentives — jitter, grinding, withholding, selfish mining, the reward design, fork/reorg depth, and organic churn (§6).
- Reproducibility and appendices — 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. 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, §8.5) — 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 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 →.
Figures
Figures are embedded from 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; that simulation folder does not commit its own generated figures — the copies checked in here are the report's figures of record.
Reproducing the results
The simulation code, configs, and run data live in tools/simulators/tsi/tsi-sim-pernode. Every study's exact command is listed in Part 4 — Reproducibility (§9). In short, from the simulator directory: make install, then make <config> to run a sweep (results land under runs/<timestamp>_<label>/), and the per-figure generators under scripts/ render the figures. Regenerated figures must be copied into report-figures/ to update this report.