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-2-14/

# Swapnil Jain: OpenAI problem #109 past 2^-14 (κ ≈ 6.397×10^-5)

Swapnil Jain (@SJ_Swapnil_Jain), X, 2026-10-08.
Source: https://x.com/SJ_Swapnil_Jain/status/2108300632738386419

## Why it matters

Seventh update: the highest claimed κ on 8 Oct, a 2^168-fold larger exponent saving than OpenAI's original, self-published and unreviewed.

## Summary

Posted 20:56 UTC on 8 Oct, after the 20:37 UTC round-seven commit (κ = 1599247689723/(2.5×10^16)). Views were still low when archived, about an hour after posting.

## Archived text

> Seventh update to OpenAI problem #109 (integer multiplication): we are now past 2^-14.
> 
> κ > 2⁻¹⁴  (tightened from κ = 2⁻¹⁸²)
> 
> The exact witness is 6.397 × 10⁻⁵, about 1.74 fold over our previous 3.667 × 10⁻⁵, 4.1 fold over round five and 8500 fold over our first witness, and a 2¹⁶⁸ fold improvement over the original OAI result.
> 
> > Quoting @SJ_Swapnil_Jain: Sixth update to OpenAI problem #109 (integer multiplication): we are now past 2^-15.

Archived 2026-10-08 via fxtwitter (unofficial).
Counts: 760 views, 58 likes, 5 reposts, 4 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/)