Not evaluated
Counterexamples to Kuznetsov's rationality conjecture (family 054)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, counterexamples to Kuznetsov's rationality conjecture, in a manuscript on irrational cubics.
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-054-counterexamples-kuznetsovs-rationality-r1
@misc{discoveria-oai-fam-054-counterexamples-kuznetsovs-rationality-r1,
author = {{DiscoverIA}},
title = {Counterexamples to Kuznetsov's rationality conjecture (family 054)},
howpublished = {DiscoverIA registry, entry oai-fam-054-counterexamples-kuznetsovs-rationality},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-054-counterexamples-kuznetsovs-rationality#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 counterexamples were valid, Kuznetsov's rationality conjecture would be false. According to its title, the manuscript concerns irrational cubic fourfolds (objects defined by an equation of degree three, in dimension four) with geometric K3 categories.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say where the question stood before the announcement.
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 · Irrational-cubic…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “Irrational cubic fourfolds with geometric K3 categories”, dated September 24, 2026. The absence of Lean is inferred from the absence of a lean/docs/054.md file; history.md reports no revision of this manuscript. 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 (Algebraic and complex geometry)
- In openai/math
- family 054, section “Algebraic and complex geometry”, 1 manuscript dated Sep 24, 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 53 of 372, by family number
- Not evaluated : Kobayashi's canonical-ampleness conjecture (family 051)
- Not evaluated : Tangent-bundle splittings and universal covers (family 052)
- Not evaluated : A counterexample to Pixton's original completeness conjecture (family 053)
- Not evaluated : Counterexamples to Kuznetsov's rationality conjecture (family 054)
- Not evaluated : Toda's Gepner conjecture and large-volume stability (family 055)
- Not evaluated : Termination of fourfold minimal model programs (family 056)
- Not evaluated : Campana's abelianity conjecture and special varieties (family 057)
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