Not evaluated
Counterexamples to Shafarevich holomorphic convexity (family 046)
The gist
In the openai/math repository released on October 6, 2026, family 046 groups 2 manuscripts on counterexamples to Shafarevich holomorphic convexity, from an unreleased internal model.
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-046-counterexamples-shafarevich-holomorphic-r1
@misc{discoveria-oai-fam-046-counterexamples-shafarevich-holomorphic-r1,
author = {{DiscoverIA}},
title = {Counterexamples to Shafarevich holomorphic convexity (family 046)},
howpublished = {DiscoverIA registry, entry oai-fam-046-counterexamples-shafarevich-holomorphic},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-046-counterexamples-shafarevich-holomorphic#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Shafarevich holomorphic convexity concerns the universal cover of a geometric space, an “unfolded” version of that space in which no loops remain. If the manuscripts were correct, they would provide counterexamples: a surface in one, a projective fourfold in the other, according to their titles.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) 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 · A-projective-fourfold…link only, reading not recorded
- Repositorygithub.com · A-surface-counterexample…link only, reading not recorded
Method
The two manuscripts are “A surface counterexample to Shafarevich holomorphic convexity” (September 23, 2026) and “A projective fourfold with large fundamental group and non-Stein universal cover” (October 5, 2026). history.md reports no revision of these manuscripts. 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 046, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 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 45 of 372, by family number
- Not evaluated : Oka classification for K3 surfaces and other compact complex surfaces (family 042)
- Not evaluated : P=W for fixed-determinant moduli spaces (family 043)
- Not evaluated : The equivariant cohomological Hikita conjecture for quivers (family 044)
- Not evaluated : Counterexamples to Shafarevich holomorphic convexity (family 046)
- Not evaluated : Complex counterexamples to cancellation and affine fibrations (family 047)
- Not evaluated : A characteristic-zero counterexample to Lipman–Zariski (family 048)
- Not evaluated : A stable-coordinate counterexample in four variables (family 049)
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