OpenAI math problem #109 tightened ~570-million-fold via nonadjacent axis swaps
aran_nayebi · x · 2026-10-08
OpenAI published a major update to math problem #109 (integer multiplication): the new bound is T(n) = O(n (log n)^(1 − κ)) with κ = 2⁻⁷⁸, tightened from 2⁻¹⁸² — roughly a 570-million-fold improvement over the previous result and 2¹⁰⁴ over the original. The earlier ceiling came from a cubic bottleneck in the network; the new witness scales quadratically and no new ceiling was established. The key was nonadjacent axis swaps, already supported by the original manuscript, cutting layout routing from O(d²) to O(d) swaps. Observers note math is now progressing "by hours, not years."
Related event: OpenAI integer multiplication bound tightened by factor of 2^104(2 posts)→
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