Not evaluated
Hyperkähler SYZ and projective-space bases (family 041)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, two manuscripts on the strong hyperkähler SYZ conjecture and on projective-space bases of Lagrangian fibrations.
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-041-hyperkahler-syz-projective-space-bases-r1
@misc{discoveria-oai-fam-041-hyperkahler-syz-projective-space-bases-r1,
author = {{DiscoverIA}},
title = {Hyperkähler SYZ and projective-space bases (family 041)},
howpublished = {DiscoverIA registry, entry oai-fam-041-hyperkahler-syz-projective-space-bases},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-041-hyperkahler-syz-projective-space-bases#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscripts were correct, they would provide, going by their titles, a result on the strong SYZ conjecture in the hyperkähler setting, and another on the case where the base of a Lagrangian fibration (a way of cutting a geometric space into pieces labelled by that base) is a projective space. The repository files this family under the section “Algebraic and complex geometry”.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no independent assessment is recorded. The sources read do not say 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 · Projective-Space-Bases-of…link only, reading not recorded
- Repositorygithub.com · The-Strong-Hyperkahler…link only, reading not recorded
Method
The two manuscripts in the openai/math repository, “Projective-space bases of Lagrangian fibrations” and “The strong hyperkähler SYZ conjecture”, are dated September 23, 2026. The repository has no lean/docs/041.md page, and OpenAI's README states “Not all have accompanying Lean formalizations.”; 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).
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 041, 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 41 of 372, by family number
- Not evaluated : Fujita's freeness conjecture (family 038)
- Not evaluated : Nagata's conjecture and maximal Seshadri constants (family 039)
- Not evaluated : Bloch's conjecture for complex surfaces (family 040)
- Not evaluated : Hyperkähler SYZ and projective-space bases (family 041)
- 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)
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