ALaleph_minus_one·Oct 21, 2026Submission
Κ = 0.003 for integer multiplication crossed
36 points · Open discussionCrocSwap
integer-mult-bounds
Python2026–2026
CrocSwap / integer-mult-bounds
integer-mult-bounds
Conditional integer multiplication: kappa > 2^-15. Community proofs, exact certificates and reproducible audits; assumes the OpenAI #109 framework.
6Distinct people
7Mentions
0Explicit recommenders
320GitHub stars
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What it is
Conditional integer multiplication: kappa > 2^-15. Community proofs, exact certificates and reproducible audits; assumes the OpenAI #109 framework.
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This week on Hacker News
Nov 7–Nov 14 UTC · Direct repository links and separately labeled related project stories. Indexed through 11/14/2026, 12:54:37 PM UTC.
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HN mentions by day7 dated mentions
Observed mentions: 2026-10-08 15:56:41 UTC to 2026-10-21 23:22:21 UTC.
Counts come from the repository’s dated source evidence. Index cutoff: 2026-11-02 08:16:59 UTC.
View mention counts and date ranges
| Period | Start (UTC) | End (exclusive, UTC) | Mentions | Submissions | Comments |
|---|---|---|---|---|---|
| Oct 8 | 2026-10-08 00:00:00 UTC | 2026-10-09 00:00:00 UTC | 2 | 1 | 1 |
| Oct 9 | 2026-10-09 00:00:00 UTC | 2026-10-10 00:00:00 UTC | 1 | 1 | 0 |
| Oct 10 | 2026-10-10 00:00:00 UTC | 2026-10-11 00:00:00 UTC | 0 | 0 | 0 |
| Oct 11 | 2026-10-11 00:00:00 UTC | 2026-10-12 00:00:00 UTC | 1 | 0 | 1 |
| Oct 12 | 2026-10-12 00:00:00 UTC | 2026-10-13 00:00:00 UTC | 0 | 0 | 0 |
| Oct 13 | 2026-10-13 00:00:00 UTC | 2026-10-14 00:00:00 UTC | 2 | 0 | 2 |
| Oct 14 | 2026-10-14 00:00:00 UTC | 2026-10-15 00:00:00 UTC | 0 | 0 | 0 |
| Oct 15 | 2026-10-15 00:00:00 UTC | 2026-10-16 00:00:00 UTC | 0 | 0 | 0 |
| Oct 16 | 2026-10-16 00:00:00 UTC | 2026-10-17 00:00:00 UTC | 0 | 0 | 0 |
| Oct 17 | 2026-10-17 00:00:00 UTC | 2026-10-18 00:00:00 UTC | 0 | 0 | 0 |
| Oct 18 | 2026-10-18 00:00:00 UTC | 2026-10-19 00:00:00 UTC | 0 | 0 | 0 |
| Oct 19 | 2026-10-19 00:00:00 UTC | 2026-10-20 00:00:00 UTC | 0 | 0 | 0 |
| Oct 20 | 2026-10-20 00:00:00 UTC | 2026-10-21 00:00:00 UTC | 0 | 0 | 0 |
| Oct 21 | 2026-10-21 00:00:00 UTC | 2026-10-22 00:00:00 UTC | 1 | 1 | 0 |
What Hacker News says
7 sourcesThe swarm's live message board is the Github PR system. The agents are dumping parallel research results including dead ends by ending the title with "(no new kappa)".
https://github.com/CrocSwap/integer-mult-bounds/pulls
In Auto Research: Integer multiplication below n log nThere is currently an effort underway to improve the bound. They have reached at a much larger kappa around 0.001635527380375392
https://github.com/CrocSwap/integer-mult-bounds
In A look at the math that OpenAI claims computes faster Fourier transforms> The sub O(nlogn) proof for DFT for example violated very old human assumptions.
btw people has massively improved the lower bound (from 1-2^-182 to about 1-2^-10) in the past couple of days: https://github.com/CrocSwap/integer-mult-bounds
In Terence Tao: Math 2.0 [pdf]Community pushed OpenAI FFT proof to over 10^-4
1 points · Open discussionThey just merged my PR for the bound on the integer multiplication problem
3 points · Open discussionThey just merged my PR for the current tightest bound on the integer multiplication problem:
https://github.com/CrocSwap/integer-mult-bounds/pull/37#even...
Something interesting happened last night: Researchers started proposing tighter conditional bounds for integer multiplication, submitted by OpenAI yesterday, then a swarm of collaborators online pushed it even further.
Its so interesting that human researchers provided the insights to push to the out-of distribution solutions that no one model reached alone.
I just submitted the current new best conditional bound, conditional κ = 4.123863984e-5, and I have a very useful system setup for auto-research that requires human intuition to reach out-of-distribution solutions.
I have a list of ideas to test so we may not be done yet :) Original paper from OpenAI: https://github.com/openai/m