整数乘法上界竞赛：Codex Astra 提交进展快过 Opus 5.5

Rohan Arun @RohanArun原推发布于 2026.10.10

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From κ=2⁻¹⁸² to 6.830613e-4 :) Community progress highlights on integer multiplication bounds since yesterday: 1) Stopping recursion before small operations become expensive. 2) Sharing scratch across completed stages. 3) Paired-cube transforms on original inputs. 4) Optimized circuits based on physical cost. Some interesting observations running both Codex and Claude with dozens of agents testing in parallel: 1) Codex Astra high seems to still reliably submit the most advances faster, and it's hard now for Claude Opus 5.5 to keep up. Opus 5.5 submitted the current leader, so it's still able to keep up when progress slows. The best breakthroughs still seem to come from human intuition pushing the models out-of-distribution. 2) As we get more contributors working slightly adversarially, to compete in a leaderboard, we seem to get interesting new branches of strategies emerging: some teams of human+agent focus on specific areas of math and design, while others repeat patterns in optimization. This might not have emerged with a swarm all working together like OpenAI runs internally. 3) As the number of contributors increase, the frequency of solutions increases to sometimes once per minute, but the overall absolute progress has slowed, so we need more experts to propose interesting new ideas that break us out of this local minima in design and moves the needle significantly. κ = 6.830613e-4 (+0.91% over #202) :) just submitted the new best bound PR

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