[pinterbanget]

Summary

This adds research/pr4586-width-growth-check/, an independent check of mihir-s-05's #4586 (head aadb7bc5): log B_N = O((1+log N)^(d+2)) for #4507's chronological batch widths. #4586 checks its lemmas on a copy of #4507's own generator. This package uses separately written code: my default-height flow (from my #4456 checks of #4436) and my width recurrence (from my check of #4507). The raw p7 rule is bound to main's higher-moment-strictification/RESULT.json. All checked claims are confirmed. No new κ.

Checks (raw p7, through rank 4000, 611,342 batch constraints)

• B_1000. It has 2,524 bits, as Prove quasipolynomial bound for chronological batch widths (no new κ) #4586 and Reduce direct-flow batch widths while preserving chronological calls #4507 report.
• Rank descent. Every recursive rank in J_n is at most ⌊(m−1)n/m⌋.
• (4). B_n | L_N^D(n) holds for every n ≤ 4000, by gcd stripping with no factoring.
• (2). The depth bound D(n) holds.
• Source-state lemma. The flow at n equals the flow at m·t, with t the largest Π-smooth integer at most ⌊n/m⌋ and Π = {2,3,5,7,11,19,41}. This holds at every rank in range.
• (5). The counting bound holds: |H(M)| = 27 ≤ 576.
• Explicit exponent. It is 211·32·45 = 303,840 at N = 1000, exactly as Prove quasipolynomial bound for chronological batch widths (no new κ) #4586 states.

python3.12 -B scripts/research_package.py --package research/pr4586-width-growth-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4586-width-growth-check outcome=completed   (~25 s, stdlib only)

Limitations:

• The written proof is Prove quasipolynomial bound for chronological batch widths (no new κ) #4586's. This package checks its finite consequences on a separate implementation.
• Physical contracts are out of scope.

Head: 2f6578907b7f8718a13921552cc3069d3908e936. Base: canonical main f626db5c.

Credit: mihir-s-05 (#4586), the #4507 width construction, and #4436's flow lineage. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code