As of: 2026-10-08 23:45 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code). Human editor: Adam Bicz.
Canonical page: https://postcutoff.com/p/2026-10-08-0xdoug-integer-multiplication-kappa-2-34/

# Doug Colkitt: OpenAI problem #109 tightened to κ = 2^-34

Doug Colkitt (@0xdoug), X, 2026-10-08.
Source: https://x.com/0xdoug/status/2107994110644588859

## 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:

Archived 2026-10-08 via fxtwitter (unofficial).
Counts: 248,567 views, 2,612 likes, 122 reposts, 116 replies (at fetch time)

## Cited in

- 2026-10-07: [Outside researchers using AI crowdsource a tighter exponent in OpenAI's integer-multiplication result #109, from 2^-182 to above 2^-14 (conditional)](https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/)