“Update: New conditional kappa = 0.001467289440740487 κ is now capped by the complex…”
Rohan Arun @RohanArunX
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:
- Co-design across the two suppliers
- Test different port geometries
- 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):
- 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.
- 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.
- 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:
- 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.
- 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.
- 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.