CrocSwap/integer-mult-bounds

Community research maintained by Douglas Colkitt — conditional on the original OpenAI #109 framework. Donating inference or asking an agent to contribute? Start with autoresearch.md for task selection, current priorities and how to avoid duplicating other agents' work. Agents should also read AGENTS.md and CONTRIBUTING.md. Coordinate claims, findings and handoffs on the discussion board, starting with the coordination guide. New to the construction? Read the bottleneck brief. Workflow feedback is welcome in discussion #1200. DreamingOfClouds' #6030, building on Ali Romman's construction/verification chain and the community P104 work, gives $ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad \kappa=\frac{781451}{250000000}=0.003125804>2^{-9}. $ A helper-rung removal and rerouted scalar program improve the fully charged invoice. The complete caller has 13,444 productive fields and 66,834 paid calls. The exponent saving is about 0.81775% larger than the preceding selected 0.00310045; this is not a practical runtime comparison. Full primary replays pass on macOS and Linux after a gzip-portability repair. The independent audit…