[pinterbanget]

Summary

This adds research/rank-convergence-gates/. It is an independent certified recomputation of zxv's #4483 (adaptive height and shifted-logarithmic majorant). That compiler is the follow-up in the maintainers' #4470 review plan; for p16 it gives sufficient rank 2^2800000000 at κ = 0.00302015.

Claim type: an independent certified recomputation. No new κ.

Results

All four BENCHMARKS.json witnesses pass every finite gate, computed with my own certified interval logarithms and exponentials. The gates are the guards (18), the mirror guard (4) on every window and t-slice, the recurrence inequality (20) and the final funding (17).

witness	D (lower)	required	final margin (lower)
p7	0.02858992	0.02336096	0.00003773
native4453	0.05448611	0.04422604	1.19575350
native4453, matched	0.05448611	0.04422604	0.32116914
p16	0.04854643	0.04306220	0.60862507

• Thin margins. p7's final margin and the τ(n₀) ≤ t_hi covers (slack 2–7·10⁻⁸) are tight but certified. PROOF.md's p7 rejection control rejects.
• Arbitrary-height flow (Remove tensor padding (199.32× smaller uniform-rank exponent) #4483's open question 1). On raw p7, at forced heights G = 0 … G₀+2 (including empty root classes), the exact rank-one identity (surplus 608), exits below n, and the exact research: #4436 boundary exits — exact mirror identity, rigorous share bound 0.321, and a correction (leaf exits dominate) #4459 mirror identity all hold, in 13 cases.

Evidence

python3.12 -B scripts/research_package.py --package research/rank-convergence-gates --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/rank-convergence-gates
  PASS_REGISTERED_RESEARCH_PACKAGE research/rank-convergence-gates outcome=completed   (~7 min, stdlib only)

Head: a1b836c56b4cd40cdad8ca84691e0e59e5d19a45. Base: canonical main f9f85c1e.

Not covered

• PROOF.md's theorem itself (the Chernoff and majorant arguments).
• The native suppliers and the consumer points.

Credit: zxv (#4483, #4436). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code