Not evaluated
Campana's abelianity conjecture and special varieties (family 057)
The gist
On October 6, 2026, OpenAI published three manuscripts, from an unreleased internal model, on Campana’s abelianity conjecture and special varieties.
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-057-campanas-abelianity-conjecture-special-r1
@misc{discoveria-oai-fam-057-campanas-abelianity-conjecture-special-r1,
author = {{DiscoverIA}},
title = {Campana's abelianity conjecture and special varieties (family 057)},
howpublished = {DiscoverIA registry, entry oai-fam-057-campanas-abelianity-conjecture-special},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-057-campanas-abelianity-conjecture-special#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
Campana’s abelianity conjecture predicts that the fundamental group of a special variety (a class of complex geometric spaces) is nearly commutative; this group is an invariant that encodes the shape of the space. If the manuscripts were correct, they would deal, going by their titles, with the case of compact Kähler manifolds, then with neighbouring cases: quasi-projective varieties and pairs of dimension 4 under an assumption.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied and no independent assessment is recorded. The sources read say neither what each manuscript claims exactly nor 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 · The-abelianity-conjecture…link only, reading not recorded
- Repositorygithub.com · Two-step-monodromy-of…link only, reading not recorded
- Repositorygithub.com · A-conditional-abelianity…link only, reading not recorded
Method
The manuscripts are “The abelianity conjecture for special compact Kähler manifolds” (September 23, 2026), “Two-step monodromy of special quasi-projective varieties” (September 24, 2026) and “A conditional abelianity theorem for special fourfold pairs with a half-weight divisor” (October 5, 2026), filed under the “Algebraic and complex geometry” section of the openai/math repository. There is no lean/docs/057.md file, 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: “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 057, section “Algebraic and complex geometry”, 3 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 4 : 4 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 56 of 372, by family number
- 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)
- 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)
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