As of: 2026-10-07 23:43 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code). Human editor: Adam Bicz.
Canonical page: https://postcutoff.com/p/2026-10-07-0xdoug-integer-multiplication-kappa-5-8e-33/

# Doug Colkitt: conditional improvement of OpenAI problem #109 (integer multiplication), κ from 2^-182 to 5.8×10^-33

Doug Colkitt (@0xdoug), X, 2026-10-07.
Source: https://x.com/0xdoug/status/2107658319632433524

## Why it matters

First announcement (02:24 UTC, ~105k views) of a conditional tightening of the exponent in OpenAI's claimed sub-n log n integer multiplication algorithm.

## Summary

First of three posts on 7 Oct. Conditional on OpenAI's algorithmic interfaces, parameter and network refinements raise the exponent saving from κ = 2^-182 to κ = 5.8×10^-33 (between 2^-108 and 2^-107); he also states a ceiling κ < 5.838×10^-33 for that network family and cost inequalities. Quotes his own 00:35 UTC thread post calling integer multiplication "probably the most shocking result" of the OpenAI release (https://x.com/0xdoug/status/2107630826636648494).

## Archived text

> We're publishing a result demonstrating a substantial tightening to the results from OpenAI Problem #109 (integer multiplication).
> 
> Conditional on OpenAI's algorithmic interfaces, our parameter and network refinements improve the exponent saving in:
> 
> T(n)=O(n(\log n)^{1-\kappa})
> 
> from κ=2⁻¹⁸² to κ=5.8×10⁻³³ (between 2⁻¹⁰⁸ and 2⁻¹⁰⁷).
> 
> This represents a nearly 2⁷⁵ fold increase in the algorithm's exponent saving parameter. 
> 
> We also establish a ceiling of κ<5.838×10⁻³³ for the stated network-counting family and cost inequalities. Our result exceeds 99% of that ceiling. Surpassing this ceiling would require improving the network bounds or cost analysis from the original result.
> 
> > Quoting @0xdoug: 3/ Integer multiplication is probably the most shocking result. Similar to matrix multiplication it’s a “asymptotic reduction”. Also like the matrix result, it’s not practical.

Archived 2026-10-07 via fxtwitter (unofficial).
Counts: 104,743 views, 198 likes, 11 reposts, 9 replies (at fetch time)

## Cited in

- 2026-10-07: [With OpenAI Codex, Doug Colkitt tightens OpenAI's sub-n log n integer multiplication exponent from 2^-182 to 2^-59 (conditional)](https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/)