Not evaluated
Oka classification for K3 surfaces and other compact complex surfaces (family 042)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript, from an unreleased internal model, titled "Every complex K3 surface is Oka".
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-042-oka-classification-k3-surfaces-other-compact-r1
@misc{discoveria-oai-fam-042-oka-classification-k3-surfaces-other-compact-r1,
author = {{DiscoverIA}},
title = {Oka classification for K3 surfaces and other compact complex surfaces (family 042)},
howpublished = {DiscoverIA registry, entry oai-fam-042-oka-classification-k3-surfaces-other-compact},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-042-oka-classification-k3-surfaces-other-compact#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A K3 surface is a type of compact complex surface, and "Oka" names a property concerning holomorphic maps (those that respect the complex structure). If the manuscript were correct, every complex K3 surface would have this property.
What remains unclear
No third-party assessment is recorded, and OpenAI supplies no Lean proof (checkable by computer) for this family. 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 · Every-complex-K3-surface…link only, reading not recorded
Method
The title of family 042 mentions K3 surfaces and other compact complex surfaces, but the openai/math repository attaches only one manuscript to it, "Every complex K3 surface is Oka", dated September 23, 2026. The absence of Lean is inferred from the absence of lean/docs/042.md; 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 042, section “Algebraic and complex geometry”, 1 manuscript dated Sep 23, 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 42 of 372, by family number
- 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)
- Not evaluated : Counterexamples to Shafarevich holomorphic convexity (family 046)
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