Not evaluated
The Kollár–Pardon universal-cover conjecture (family 058)
The gist
In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, to have obtained results on the Kollár–Pardon conjecture about universal covers.
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-058-kollarpardon-universal-cover-conjecture-r1
@misc{discoveria-oai-fam-058-kollarpardon-universal-cover-conjecture-r1,
author = {{DiscoverIA}},
title = {The Kollár–Pardon universal-cover conjecture (family 058)},
howpublished = {DiscoverIA registry, entry oai-fam-058-kollarpardon-universal-cover-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-058-kollarpardon-universal-cover-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 two manuscripts were correct, they would establish results on semialgebraic universal covers (described by polynomial equations and inequalities) of normal projective varieties, and on the symmetry of semialgebraic bounded domains with compact quotient.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) supplied by OpenAI itself is marked as unchecked in its tracking file, and no third-party verification 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 · 058.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 · Semialgebraic-universal…link only, reading not recorded
- Repositorygithub.com · Symmetry-of-semialgebraic…link only, reading not recorded
- Lean proofgithub.com · 058.mdpage read word for word
- Lean proofgithub.com · SymmetricDomains.leanlink only, reading not recorded
Method
The openai/math repository contains two manuscripts dated September 24, 2026: “Semialgebraic universal covers of normal projective varieties” and “Symmetry of semialgebraic bounded domains with compact quotient”. The file lean/docs/058.md describes the Lean formalisation with one Comparator statement (lean/ComparatorChallenges/SymmetricDomains.lean); the family is among the sources of formalization.yaml, and 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. 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 (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Algebraic and complex geometry)
- In openai/math
- family 058, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 5 : 1 read word for word, 4 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 57 of 372, by family number
- 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)
- Not evaluated : The Kollár–Pardon universal-cover conjecture (family 058)
- Not evaluated : Counterexamples to Zariski's multiplicity conjecture (family 059)
- Not evaluated : The Global Spherical Shell conjecture (family 060)
- Not evaluated : The LeBrun–Salamon conjecture and projective contact classification (family 062)
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