Doug Colkitt: OpenAI problem #109 tightened to κ = 2^-34
Doug Colkitt @0xdougX
Why it matters
Colkitt’s fourth result (~249k views), the 48-million-fold jump that Jain and others then built on.
Summary
Posted 00:38 UTC on 8 Oct, after the 00:27 UTC commit ‘Publish conditional compact-control bound beyond 2^-34’ (κ = 83/10^12). Done with OpenAI Codex per the repository; conditional on OpenAI’s manuscript.
Archived text
We are publishing an update to OpenAI problem #109 (integer multiplication) with further tightening.
κ = 2⁻³⁴ (tightened from κ = 2⁻¹⁸²)
The exact witness is 8.3 × 10⁻¹¹, a roughly 48 million fold improvement over the previous result and a 2¹⁴⁸ fold improvement over original OAI result.
The improvement came from removing the spacing penalty behind the quadratic bottleneck. This was done by moving compact control bits instead of entire windows.
Quoting @0xdoug: We are publishing an update to OpenAI problem #109 Integer multiplication) with another substantial further tightening: