[pinterbanget]

Summary

This adds research/gauge-column-check/. It is an independent check of jwr404's #4438, the within-cell gauge column transfer for diag(â)Ĝdiag(â)^{−1}.

Claim type: an independent check by separate code, with exact rationals where possible. No new κ.

Results

All of #4438's statements check out.

• Factorization. n_{i,h} = (a_i/a_{i+h})exp(−aρh²) with a_i = exp(aβ_i²/θ). It holds on 2,000 random constant-phase runs from LOG-A's entry law, with log error ≤ 6·10⁻¹³.
• Column bound. The 1/(1−ε) bound holds on the random rounded blocks, with maximum ratio 0.99977, so it is nearly tight.
• Ceiling. The gap is exactly 1/(16p²−1) at ε = 1/(16p²), and ε = 1/2 leaves none.
• Setup constant. C = 3 is the least integer with 2^{−Cp} ≤ 1/(16p²). Note that it holds with equality at p = 2, so there is no slack there.
• Downstream comparison. p(2p−1) > 2 holds.

Evidence

python3.12 -B scripts/research_package.py --package research/gauge-column-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/gauge-column-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/gauge-column-check outcome=completed   (~1 s, stdlib only)

Head: baf56b163de5981ade5afa28f75bbd7e019f8b65. Base: canonical main 2a13eb18.

Credit: James Reed (jwr404, #4438). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code