[pinterbanget]

Summary

This adds research/direct-flow-width-check/. It is an independent check of zxv's #4436 §3 (nested widths and complete count bounds) on raw p7. That section was left uncovered by my #4456, whose flow implementation this reuses.

Claim type: an independent finite check plus an exact counting identity. No new κ.

Results (every rank 121 ≤ n ≤ 2000)

• Width factor. S_n ≤ C = W(W+P+1)^{h+1}, with W = 7688 and P = 55998. The worst S_n/C is 1.6·10⁻⁵.
• New exact identity. sources + exits + 2·matched = U(W+P). So Bound compiler width by exp(O(N log N)) and route overlapping ranks #4436's routing count equals 2(W+P)U − 2·matched exactly, and is at most 2(W+P)U.
• Growth. log B_N/(N log N) is 1.09, 1.76, 1.96 and 2.03 at N = 500, 1,000, 1,500 and 2,000, and 2.07 at 3,000 locally. That is consistent with exp(O(N log N)), with a constant near 2.

Evidence

python3.12 -B scripts/research_package.py --package research/direct-flow-width-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/direct-flow-width-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/direct-flow-width-check outcome=completed

Head: 4e7022aa9128c8673d3e2024052b2deaa18cb6e4. Base: canonical main 2a13eb18.

Credit: zxv (#4436) and Jacob Alan Sussman (Theorem 1G). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code