OpenAI Problem #109 Tightened by ~570M-Fold: New κ=2^-78 via Nonadjacent Axis Swaps
aran_nayebi · x · 2026-10-07
0xdoug's team published a substantial tightening of OpenAI Problem #109 (integer multiplication): conditioning on OpenAI's algorithmic interfaces, the exponent-saving parameter κ in T(n)=O(n(log n)^(1−κ)) improves from 2⁻¹⁸² to about 2⁻⁷⁸ — roughly a 570-million-fold gain over their prior result and 2¹⁰⁴ over the original OpenAI result. The key was nonadjacent axis swaps routing around a cubic bottleneck, cutting layout routing from O(d²) to O(d) swaps. The new witness scales quadratically, so the earlier ceiling no longer applies and no new ceiling has been established.
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