4baccd8d4b
The unpaired comparison could not answer the question it was asked. The two uncle models draw independent RNG streams -- uncle_model is in the config key, which is what makes --old bit-reproduce earlier runs -- so the arms differed in stake draw, peering graph and every lottery outcome, each comparison paid the between-run variance twice, and the per-cell floor (+-0.0015) sat an order of magnitude above the effect. Only delta_max = 5 resolved, and only after pooling. Adds `paired_streams`: the RNG root is derived from the model- independent part of the key, so a countable cell and its --old twin get the SAME stake, graph and lottery draws and the uncle rule is the only difference. Each replicate is then a matched pair and the shared variance cancels. Trajectories still diverge after epoch 0 through the genuine feedback (a different counted density changes the next epoch's difficulty), which is the signal. The flag is deliberately NOT in key(): it selects which key the seed is derived from, so including it would perturb every historical seed. Re-verified that --old still bit-reproduces the committed 2026-07-27 rho-boundary parquet, max |delta| = 0. Results (configs/fine-delay-paired.yaml, 40 replicates per arm): - Negative control becomes an IDENTITY check. With U = 0 no reference is taken, so shared streams must give bit-identical trajectories. All 200 replicate pairs differ by exactly 0.0. Unpaired, the same control only had to agree within +-0.025 and drifted by 0.016. - Per-cell SE shrinks by a median 1.6x (1.2-2.1x); widest 95% CI goes +-0.0015 -> +-0.0010. 5/15 cells resolve at |t| >= 2 (0.75 expected by chance); the largest, U=2 at delta_max=4, is t = 4.32 and clears Bonferroni for 15 tests. - The cost is a STEP, not the ramp the unpaired data suggested: delta_max 1-3 unresolved (t = 1.1, 1.8, 1.4), then delta_max 4 AND 5 both resolve at -0.0011 (t = 4.7) and -0.0009 (t = 3.7). Whole-band pooled -0.00060 +- 0.00021, t = 5.7 -- where the unpaired estimate of the same quantity (t = 2.8) had failed correction. So the first-fork restriction costs nothing measurable up to delta_max = 3 and about 0.1% at 4-5 -- an order of magnitude below the +-0.9% per-epoch sampling noise. Two bugs found while building this, both of which would have silently produced a wrong answer: - paired_streams was missing from metrics._CONFIG_FIELDS, so it never reached the parquet; plot_fine_delay.py falls back to the unpaired test when it cannot confirm pairing, so the sweep would have completed and quietly reported the old result. Caught before the run finished; the sweep was restarted and a test now pins the field. - The U=0 control check reported FAILS on a PERFECT control: paired, the gap is exactly 0 so its SE is 0 and t is 0/0. It now checks the gap itself when the streams are shared, and falls back to the t-test only when there is real spread. §3.2a is rewritten around the paired measurement; the unpaired sweep is retained in §9 as the power comparison that motivated it. Figures 34-35 regenerated, with the control annotation and provenance reflecting the design actually used. Tests: 214 passed (was 209). 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. The whole report is one document — 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 regimeρ < 1and diverge only under overload. See the model note at the top of the report, the mechanism in §2.1, the comparison in §3.2–§3.2a, and the reproduction notes in §9.
Contents
| § | what it covers |
|---|---|
| §1 | executive summary — the problem, the findings, the recommendation |
| §2 | the model, the measurement convention, and the counting rule |
| §3 | the findings and their evidence, including the high-precision design band (§3.2a) |
| §4 | design equations and the parameter-selection algorithm |
| §5 | caveats and regime of validity |
| §6 | robustness — jitter, grinding, withholding, selfish mining, rewards, reorg depth, churn |
| §7 | parameter reference — what each knob does |
| §8 | the safest selection, residual risks, and the recommendation-vs-spec deltas |
| §9 | reproducibility — how to re-run every study |
| A · B · C | 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, §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 §8 →.
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 §9 — Reproducibility. 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.