feat(science): corpus sizing by seeded power analysis — Phase A6

[pixelstrade-dev]

Phase A6 of the validity program — corpus sizing derived, not decreed

The growth plan inherited a "2 000–5 000 items" corpus target chosen by round number. This PR replaces it with numbers derived from committed Run 001 parameters, via seeded simulations that anyone can reproduce.

New module: lib/statistics/simulation.ts (mirrored to @caims/core)

• mulberry32(seed) — deterministic PRNG; makeNormalSampler — Box–Muller with spare caching.
• boundDetectionPower({sigma, delta, n, sims, seed}) — P(mean of n samples flags a true bound violation of Δ). Anchored against the analytic answer Φ(√5) ≈ 0.987.
• bootstrapHalfWidth({observed, itemCount, stat, sims, seed}) — 95 % CI half-width of a statistic under item resampling; returns null (never a fake number) when the statistic is mostly undefined.
• 11 tests including the analytic anchor, determinism, monotonicity, and the null-honesty cases.

New CLI + report: cli/power-analysis.ts, docs/power-analysis-a6.md

All parameters from run-001/results/summary.json (seed 20260823, 20 000 sims):

• Samples per cell: n=5 already gives ≥ 0.93 power for ≥ 5-point bound violations even at the adversarial-worst σ=7.60. Chasing 2-point violations would need n=25 — the honest alternative is preregistering bounds so a meaningful violation is ≥ 5 points.
• Judge-drift precision: ~100 all-judge items pin mean |judge diff| to ±1.7 pts.
• α precision: adversarial strata dominate the cost (±0.15 at 100 items, and those half-widths are labeled optimistic lower bounds — the bootstrap resamples only 5–6 observed values).
• Recommendation — corpus v1: ~200–300 items, 25–30 % adversarial, n=5, ≥ 3 judge families (≈ 3 750 calls/run). The 2 000–5 000 scale is re-sized only after Run 002 provides real 3-rater data — 3-rater sizing from 2-rater data would mean inventing a judge.

Orchestrator review — applied fixes

Adversarial review returned APPROVED WITH REQUIRED FIXES; all applied:

• MAJOR: doc table labeled σ=2.05 while the CLI simulated at rounded σ=2.0, and the even-count median was the upper-middle element, not interpolated. Fixed: interpolated median (1.92), simulations at unrounded σ, labels via toFixed(2) — the table now states exactly what was simulated.
• "Nothing is assumed that the run did not measure" was false (normality is assumed) → "no parameter is invented", with modeling assumptions listed.
• Bit-for-bit reproducibility scoped to Node (Math.log/sin/cos are not bit-specified by IEEE 754).
• All-1.000 saturated rows included; controls median α ≈ 0.159 cross-referenced to the A5 disaggregated analysis.

Validation

• apps/web: 374/374 tests; packages/core: 187/187; cold tsc clean on core and on all touched files (the only web errors are the pre-existing Prisma-generated-client absence in this container — CI regenerates it).
• sync-core drift check clean.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Y7wiMwFa2D4P8zD9RhCgsv

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Generated by Claude Code