Not evaluated
Claimed proof of the Unique Games Conjecture (family 102)
The gist
In its release of October 6, 2026, OpenAI claims to have proved the Unique Games Conjecture (UGC), linked to optimal approximation thresholds.
DiscoverIA status on October 11, 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 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-102-unique-games-r1
@misc{discoveria-oai-fam-102-unique-games-r1,
author = {{DiscoverIA}},
title = {Claimed proof of the Unique Games Conjecture (family 102)},
howpublished = {DiscoverIA registry, entry oai-fam-102-unique-games},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-102-unique-games#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If this proof held, the conjecture (a statement believed true but not yet proved) would become a theorem. The family's title links it to these thresholds, that is, to the best accuracy an efficient algorithm can guarantee, without saying which ones.
What remains unclear
No third party is recorded as a checker, and the Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself. On his blog, Scott Aaronson writes that “no human has understood just about any of these proofs yet”. He also quotes Dana Moshkovitz, for whom it would be “impossible to read it without AI help”; the sources read give no link for this remark and do not say what “it” refers to.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · scottaaronson.blog
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.comlink only, reading not recorded
Method
OpenAI publishes the preprint “The Unique Games Theorem” and a summary of the reasoning for family 102. A Lean file supplied by OpenAI is listed: its title appears in formalization.yaml:812, with the configuration UniqueGamesTheorem. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from scottaaronson.blog (page read, quotation checked word for word: “no human has understood just about any of these proofs yet”).
Limits
The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Theoretical computer science
- Checked by
- claimant; no third party
- Sources
- 1 : 1 link only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
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 99 of 372, by family number
- Not evaluated : The sharp distortion of edit distance into ℓ_1 (family 099)
- Not evaluated : A counterexample to Bang's cylinder-covering bound (family 100)
- Not evaluated : The sharp simplex conjecture for isotropic constants (family 101)
- Not evaluated : Claimed proof of the Unique Games Conjecture (family 102)
- Not evaluated : Derandomization of logarithmic space: L=RL=BPL (family 103)
- Not evaluated : Quasipolynomial algorithms for mean-payoff, stochastic and parity games (family 104)
- Not evaluated : The 2-to-1 Games Conjecture with perfect completeness (family 105)
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