Not evaluated
Integer multiplication below n log n
Family 109
The gist
On October 6, 2026, OpenAI released a manuscript claiming integer multiplication below the n log n mark, where n is the size of the integers.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
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-oai-fam-109-integer-multiplication-below-n-n-r1
@misc{discoveria-oai-fam-109-integer-multiplication-below-n-n-r1,
author = {{DiscoverIA}},
title = {Integer multiplication below n log n (family 109)},
howpublished = {DiscoverIA registry, entry oai-fam-109-integer-multiplication-below-n-n},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-109-integer-multiplication-below-n-n#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript held, the computing cost of multiplying two integers of size n would grow more slowly than n log n as the integers get longer. Here, log denotes the logarithm.
What remains unclear
No independent assessment is recorded, and OpenAI provides no Lean proof (Lean is a language in which a computer checks every step of a proof) for this family. The result comes from an internal model that OpenAI has not released.
In the glossary : n log n and κ
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
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 · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Integer-multiplication…link only, reading not recorded
Method
In the openai/math release, family 109 has a single manuscript, “Integer multiplication below n log n”, dated September 23, 2026. It is filed under the section “Theoretical computer science” of overview.tex; history.md reports no revision. 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Theoretical computer science
- In openai/math
- family 109, section “Theoretical computer science”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 106 of 372, by family number
- Not evaluated : Hardness of coloring three-colorable graphs (family 106)
- Not evaluated : Matrix multiplication exponent at most 9/4 (family 107)
- Not evaluated : A cubic permanent–determinant lower bound (family 108)
- Not evaluated : Integer multiplication below n log n (family 109)
- Not evaluated : Optimal-order randomized k-server on arbitrary metrics (family 110)
- Not evaluated : One-sample matroid prophet inequalities against an almighty adversary (family 111)
- Not evaluated : Beyond the square-root exponent for depth-three circuits (family 112)
Related frontiers
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