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-2-18/

# Swapnil Jain: OpenAI problem #109 past 2^-18 ('2^-1x territory')

Swapnil Jain (@SJ_Swapnil_Jain), X, 2026-10-08.
Source: https://x.com/SJ_Swapnil_Jain/status/2108136796886548867

## Why it matters

Highest-reach post (~135k views) of Swapnil Jain's series; at the time it claimed about 2.2 times the strongest open result.

## Summary

Posted 10:05 UTC on 8 Oct, matching the round-three commit at 10:03 UTC in github.com/Swapnil-jain/integer-mult-kappa. Conditional on OpenAI's unverified manuscript; the repository says the work was done with assistance from Claude (Anthropic).

## Archived text

> We are publishing a third update to OpenAI problem #109 (integer multiplication), and we have now entered 2^-1x territory.
> 
> κ > 2⁻¹⁸  (tightened from κ = 2⁻¹⁸²)
> 
> The exact witness is 4.19 × 10⁻⁶, roughly 558 fold over our previous 7.5 × 10⁻⁹, about 2.2 fold over the strongest open result, and a 2¹⁶⁴ fold improvement over the original OAI result.
> 
> > Quoting @SJ_Swapnil_Jain: We are publishing a second update to OpenAI problem #109 (integer multiplication), building on Doug Colkitt's results, with further tightening.

Archived 2026-10-08 via fxtwitter (unofficial).
Counts: 134,870 views, 1,309 likes, 39 reposts, 24 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/)