As of: 2026-10-12 22:30 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code). Human editor: Adam Bicz.
Canonical page: https://postcutoff.com/p/x-rohanarun-2109466530219999637/

# “Update: New conditional kappa = 0.001467289440740487 κ is now capped by the complex…”

Rohan Arun (@RohanArun), X, 2026-10-12.
Source: https://x.com/RohanArun/status/2109466530219999637

## Archived text

> Update: New conditional kappa = 0.001467289440740487
> 
> κ is now capped by the complex supplier: b ≈ 1.460e-3 against the bit side’s c ≈ 1.565e-3.
> 
> The hosting tricks are nearly exhausted with this construction, so the gains have to come from the complex local word or its geometry.
> 
> I'm first testing a solver/perturbations trick I used in training LLMs between pre-training steps that actually works, which could save us 3% on κ.
> 
> Further ideas: 
> 1) Co-design across the two suppliers
> 2) Test different port geometries 
> 3) Test a third supplier
> 
> I'm testing publishing findings so agents can collaborate across teams here: https://github.com/rohanarun/integer-mult-bounds/tree/research/findings-2026-10-12/research/experiment-log
> 
> Feel free to add/use it. 🫡
> 
> https://github.com/CrocSwap/integer-mult-bounds/pull/527
> 
> > Quoting @RohanArun: From κ=2⁻¹⁸² to 0.001289283116 :)  
> > 
> > Integer multiplication community auto-research highlights since yesterday (+69.13% in 24 hours):
> > 
> > 1) We had multiple flips of the infamous "wall" between the bit side and complex side thanks to community efforts.
> > 
> > Yesterday we put out a call for researchers to submit wild new designs, and multiple experts submitted :) 
> > 
> > @mrowdays was responsible for most of the limit increase in the last day and introduced Sussman's E8 geometry.
> > 
> > 2) We switched to E8 geometry. (Thanks to Jacob Sussman for the E8 unit)
> > 
> > E8 is a symmetric lattice in eight dimensions, and Sussman’s E8 construction was adapted by contributors on both the complex and bit sides.
> > 
> > It's wild that it even works, but I'm noticing cross-pollination across breakthroughs now that agents can accelerate the insights. Humans still seem to connect the disparate dots most often.
> > 
> > 3) We crossed κ = 10⁻³, and Dugongue posted the first PR around 3 a.m.!
> > 
> > Much of the progress in the last day came from optimizing and canceling existing parts of the algorithm.
> > 
> > Interesting observations:
> > 
> > 1) We started sharing notes across agent teams and published GitHub files with failures to avoid repeating tokens.
> > 
> > Competition seems to drive a lot of the progress, since it's exciting to participate like in sports, so we're testing if agent teams progress faster collaborating or if competing is somehow driving faster progress.
> > 
> > It's possible researchers wouldn't have noticed this if there weren't such attention, and winning the leaderboard is a root human incentive.
> > 
> > 2) We analyzed all the agent PR data:
> > 
> > 151 PRs opened in the last 24 hours: 89 disclose Codex and 48 disclose Claude.
> > 
> > 261,895,084 lines of code added; 37,108 deleted.
> > 
> > Most prolific contributors: rohanarun with 118 PRs, eumemic with 73, and chafreaky with 63.
> > 
> > Codex published the most advances, but all the top human-agent teams use both Codex and Claude to generate fresh ideas.
> > 
> > Some teams are using Antigravity, Cline, Hermes, and even ChatGPT to submit progress!
> > 
> > Experts with good intuition can use any harness, but frontier models save hours, so they're winning early progress.
> > 
> > 3) Researchers are tightening bounds across multiple other papers now, like the Quasi-Riemann hypothesis, and applying breakthroughs across papers.
> > 
> > A handful of experts joined the battle in the last day, and multiple others got inspired to submit solutions to other papers, like @HaileyStormC’s submission to QRH.
> > 
> > Auto-research is just beginning, and anyone can copy the prompt on this site to contribute with Codex or Claude: http://app.getsupers.com/auto-research
> > 
> > I'm having a call with top contributors Monday to share best practices, and I'll record and publish the highlights to encourage more to join us.
> > 
> > If you're not sure where to start and want to get involved in auto-research, feel free to DM me. 
> > 
> > The only requirement to get invovled is good intuition and a subscription to Codex/Claude. 
> > 
> > We need more human intuition to guide the agents and connect the dots, and there's likely breakthroughs just waiting to be prompted. 
> > 
> > Conditional κ ≈ 0.001289283116 :) Just submitted a new best bound.
> > 
> > https://github.com/CrocSwap/integer-mult-bounds/pull/467

Archived 2026-10-12 via fxtwitter (unofficial).
Counts: 12,147 views, 106 likes, 3 reposts, 2 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 about 2^-9.4 (conditional)](https://postcutoff.com/e/2026-10-07-colkitt-codex-integer-multiplication-exponent/)