Not evaluated
Hindman's finite sums and products conjecture (family 164)
The gist
On October 6, 2026, OpenAI released a manuscript on monochromatic finite sums and products of positive integers, tied to Hindman's conjecture.
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-164-hindmans-finite-sums-products-conjecture-r1
@misc{discoveria-oai-fam-164-hindmans-finite-sums-products-conjecture-r1,
author = {{DiscoverIA}},
title = {Hindman's finite sums and products conjecture (family 164)},
howpublished = {DiscoverIA registry, entry oai-fam-164-hindmans-finite-sums-products-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-164-hindmans-finite-sums-products-conjecture#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, it would bring a result on finite sums and products of positive integers that all have the same colour (the manuscript title says “monochromatic”). The family is tied to Hindman's conjecture, a statement in combinatorics.
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 manuscript comes from an internal model that OpenAI has not released.
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 · Monochromatic-finite-sums…link only, reading not recorded
Method
In the openai/math release, family 164 has a single manuscript, dated September 23, 2026: “Monochromatic finite sums and products in the positive integers”. It is filed under the section “Combinatorics” 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
- Mathematics (Combinatorics)
- In openai/math
- family 164, section “Combinatorics”, 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 158 of 372, by family number
- Not evaluated : Superexponential van der Waerden numbers (family 160)
- Not evaluated : Counterexamples to Sidorenko's conjecture and the forcing conjecture (family 161)
- Not evaluated : Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures (family 162)
- Not evaluated : Hindman's finite sums and products conjecture (family 164)
- Not evaluated : Exact crossing numbers of complete and complete bipartite graphs (family 165)
- Not evaluated : The higher-dimensional Erdős distinct-distances conjecture (family 166)
- Not evaluated : Pinned distances and a power saving for planar unit distances (family 167)
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