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-sj-swapnil-jain-integer-multiplication-kappa-2-27/

# Swapnil Jain: OpenAI problem #109 tightened to κ = 2^-27, building on Colkitt

Swapnil Jain (@SJ_Swapnil_Jain), X, 2026-10-08.
Source: https://x.com/SJ_Swapnil_Jain/status/2108109123774796281

## Why it matters

Earliest X update we found in Swapnil Jain's parallel Claude-assisted series; it explicitly builds on Doug Colkitt's results.

## Summary

Posted 08:15 UTC on 8 Oct. Called his 'second update'; the repository shows his first witness, 249/(5×10^10) ≈ 4.98×10^-9, committed at 07:17 UTC, and this 7499/10^12 witness at 07:29 UTC. Quotes Colkitt's 2^-34 post. We did not find his first X update.

## Archived text

> We are publishing a second update to OpenAI problem #109 (integer multiplication), building on Doug Colkitt's results, with further tightening.
> 
> κ = 2⁻²⁷  (tightened from κ = 2⁻¹⁸²)
> 
> The exact witness is 7.499 × 10⁻⁹, a roughly 1.5 fold improvement over our previous 4.98 × 10⁻⁹, 90 fold over Colkitt's 8.3 × 10⁻¹¹, and a 2¹⁵⁵ fold improvement over the original OAI result.
> 
> > Quoting @0xdoug: We are publishing an update to OpenAI problem #109 (integer multiplication) with further tightening.

Archived 2026-10-08 via fxtwitter (unofficial).
Counts: 63,277 views, 63 likes, 2 reposts, 1 reply (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/)