[pinterbanget]

Summary

This adds research/column-cut-check/. It is an independent numerical check of jwr404's #4437: the ideal column majorant e^{−2aθ} + e^{−2a(1−θ)} + 2e^{−2a}/(1−e^{−4a}) holds for every column of the ideal narrow matrix, including g = 2 steps.

Claim type: an independent numerical check with explicit tolerances. No new κ.

Results

The matrix is built directly from LOG-A's entry law, not from #4437's code.

• Majorant. 192,000 interior columns, 55,515 of them meeting g = 2, are all within the majorant. The grid covers p ∈ {2,3,5,10}, a at both GAUSSIAN ends and three values outside, four θ, and 20 phases. A local run of 704,000 columns agrees.
• Sharpness. The majorant is attained: the maximum ratio is 1.0 to floating precision.
• Landing intervals. Extend the ideal column majorant across every legal g=2 step (no new κ) #4437's table of incoming/outgoing g against β_j holds at every column.
• Gap. 1 − M > 1/(8p²) at the worst corners for every p up to 10⁴, with minimum 8p²·gap = 26.3. The perturbation step holds as well.

Evidence

python3.12 -B scripts/research_package.py --package research/column-cut-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/column-cut-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/column-cut-check outcome=completed   (~5 s, stdlib only)

Head: b5f7fbbb4a4a778f78da69ee1a5d965a6af081ad. Base: canonical main 2a13eb18.

Not covered

• An all-p proof of the gap; Extend the ideal column majorant across every legal g=2 step (no new κ) #4437's written argument covers that.
• The rounded H.
• Any new κ.

Credit: James Reed (jwr404, #4437, building on #4402). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code