[cyc6221]

Summary

Updates _articles/Math/ai/openai/integer-mult-bounds.md to the CrocSwap/integer-mult-bounds state as of 2026-10-29. The selected result moved from CrocSwap/integer-mult-bounds#5599 (κ = 0.00310045) to CrocSwap/integer-mult-bounds#6030 (κ = 781451/250000000 = 0.003125804), selected 2026-10-28.

• Status and summary sections: #6030 is now the current selected throughout: the status table, the main-progression summary and table, the milestones table, the techniques list, the bottleneck comparison and the retained assumptions. Notes that Conditional κ = 0.003127804 (+6.67e-7 over #6143): remove the 772/731 relay CrocSwap/integer-mult-bounds#6145 (κ = 0.003127804) is merged but only partially reviewed.
• New subsection #5599 → #6030: the candidate chain on the P104 word (#5627 through #5907), the #6030 helper-470 rung removal and its gain $H_1+H_3-H_4$, credits, and verification (#5960 independent audit, caller positive control, crossing interval, #6043 corroboration).
• References: #6030 application review and integration receipt, 15 chain PRs through #6145, and the #5550 / #5960 / #6043 independent checks.

Test plan

• bundle exec jekyll build

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[cyc6221]

Code review fixes, pushed in a41a3d7 and 0c289ed:

• #5960 attribution (a41a3d7): Independent replay, invoice, native and funding audit of #5827 and #5907 (no new κ) CrocSwap/integer-mult-bounds#5960 audits #5827 and #5907, not #6030. The note now says the maintainer's #6030 application review reuses #5960's independent interpreter. The scope paragraph also notes that #6030 went through an application review, not a proof review.
• P104 subsection (0c289ed):
  • Per-step gains are now given as $10^{-7}$ to $10^{-5}$; 6 of the 15 steps exceed $10^{-6}$.
  • The gain is stated as "helper change minus paid change" = $H_1+H_3-H_4$.
  • The #6030 edit now also lists helper 704's new path, the rerouted 560/268 read, and the itinerary changes for helpers 115, 713 and 736 and for Y main 127.
  • "最後" before #5599 is now "接著", since #6030 continues the same chain.

Not changed: #6143 stays out of the references because it was closed unmerged and the list only covers merged PRs.