Not evaluated
Conditional integer-multiplication bound κ ≈ 0.00139
Integer-mult-bounds PR #514
The full story, in French: Multiplying two large numbers faster than n log n
Current record on the frontier: 0.015637149091, as of Oct 22, 2026. See the frontier and the record history
The gist
On October 11, 2026, a contributor to the integer-mult-bounds project proposed a conditionally improved theoretical bound for multiplying very large integers.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
Text written by an AI, reviewed by Antoine Olivier,
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-imb-pr514-kappa-2026-10-11-r1
@misc{discoveria-imb-pr514-kappa-2026-10-11-r1,
author = {{DiscoverIA}},
title = {Conditional integer-multiplication bound κ ≈ 0.00139 (integer-mult-bounds PR #514)},
howpublished = {DiscoverIA registry, entry imb-pr514-kappa-2026-10-11},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/imb-pr514-kappa-2026-10-11#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
κ appears in a theoretical bound on computing time, of the form n (log n)^(1-κ) for n-bit numbers (binary digits): the larger κ, the lower this bound as n grows, with no promise of a practical speed-up. If the bound held, it would improve, under the same assumptions, on the one in family #109 of the OpenAI release, where κ = 2^-182, a far smaller number.
What remains unclear
The result only stands if the framework of OpenAI family #109 and the interfaces listed by the PR (a change request on GitHub) are sound. No published independent evaluation is recorded and the request is not merged. No AI use is declared in this PR: the entry is tracked because it builds on that OpenAI result.
In the glossary : Bound, n log n and κ, Reproduction
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 514
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
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What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · 514page read word for word · consulted on Oct 12, 2026
- Repositorygithub.com · integer-mult-boundspage read word for word · consulted on Oct 12, 2026 ·
Community research maintained by Douglas Colkitt — conditional on the original OpenAI #109 framework.
- Papergithub.com · CONTENTS.mdpage read word for word · consulted on Oct 12, 2026 ·
109. Integer multiplication below $`n\log n`$. Multiplies two n-bit integers exactly at every input length in deterministic worst-case time $`O(n(\log n)^{1-\kappa})`$, with $`\kappa=2^{-182}`$
Method
The PR provides a finite certificate in exact rational numbers, which the verify.py script replays using only the Python standard library. κ is exactly 1391523459591829/1000000000000000000, under the assumptions of the OpenAI #109 framework adopted by the PR. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word).
Limits
DiscoverIA has recorded no independent evaluation as of this date. Antoine Olivier contributed to the integer-mult-bounds repository (PR #214).
Key facts
- Claimed by
- a contributor (contributor to CrocSwap/integer-mult-bounds) (Name replaced by a role)
announced on Oct 11, 2026 - Nature
- new result
- Field
- Theoretical computer science (complexity of integer multiplication)
- Checked by
- claimant
- Sources
- 3 : 3 read word for word
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
Status history
Only one observation so far.
An observation is added; none is ever erased.
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