[pinterbanget]

Summary

This adds research/delta-halo-exponent-check/. It is an independent check of jwr404's #4451 and #4452: the within-cell halo exponents 11, 24, 26, 26 and 6 under the published weight error δ = 2^{2−32760p}.

Claim type: an independent check, by a separate proof route plus exact rational replay. No new κ. The ideal gaps 1/(8p²) stay hypotheses.

Results

• The relative-error repair a/â < 1/(1−δ) holds, and δ < 1/(16p²) (The published 4η weight error meets the 1/(16p^2) ratio budget (no new κ) #4451).
• The Neumann ceiling. (1−δ)/(g−δ) = U = 8p²(D−4)/(D−32p²) holds exactly.
• For all p ≥ 2, by a different route (p < 2^p, so 32p²/D < 1/(16p²)): 8p² < U < V < 8p²+1 ≤ 16p²−1 < p⁶ and V² < p^{11}.
• The series error at L = p^{24} is below p⁶e^{−p²}, and the bandwidth is below p^{26}.
• Exact replay. Every inequality is checked with Fraction for p from 2 to 64.
• The "fails" column is confirmed at p = 2.

All five exponents are confirmed.

Remarks

• Bandwidth at p = 2. The sharp count there is 2^{25}−1 < p^{25}. "25 fails" at p = 2 therefore holds only for the loose count. The sharp count fails for p ≥ 3, and Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new κ) #4452's text already says this.
• Unit diagonal. Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new κ) #4452's lemma relies on Ĝ_0 = 1, inherited from Bound the within-cell column gap by a relative weight error of 1/(16p^2) (no new κ) #4438/Apply the smaller halo exponents inside one cell, with normalizer 6 (no new κ) #4439, without restating it.

Evidence

python3.12 -B scripts/research_package.py --package research/delta-halo-exponent-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/delta-halo-exponent-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/delta-halo-exponent-check outcome=completed   (~20 s, stdlib only)

Head: 6aaf48105c2100d0dcf47b5b1ff5a85c37ddef52. Base: canonical main 2a13eb18.

Not covered

• The ideal gaps.
• Across-cell transfer (Apply the smaller halo exponents across a cell, under the downward reading (no new κ) #4442, Prove the downward rounding contract for across-cell Gaussian entries #4449).
• Any new κ.

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

🤖 Generated with Claude Code