Not evaluated
Bloch's conjecture for complex surfaces (family 040)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on Bloch's conjecture for complex surfaces with p_g equal to 0.
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-040-blochs-conjecture-complex-surfaces-r1
@misc{discoveria-oai-fam-040-blochs-conjecture-complex-surfaces-r1,
author = {{DiscoverIA}},
title = {Bloch's conjecture for complex surfaces (family 040)},
howpublished = {DiscoverIA registry, entry oai-fam-040-blochs-conjecture-complex-surfaces},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-040-blochs-conjecture-complex-surfaces#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
According to its title, the manuscript concerns Bloch's conjecture for complex surfaces with p_g equal to 0; its exact scope is not specified in the sources read. If the manuscript were correct, it would bring a result on this conjecture. The number p_g is a number attached to a complex surface (its geometric genus).
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The manuscript's title speaks of surfaces with p_g=0, while its folder name speaks of surfaces with p_g=q=0: the sources read do not say which exact case is treated.
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 · Blochs-Conjecture-for…link only, reading not recorded
Method
In the openai/math repository, family 040 comprises one manuscript, “Bloch’s conjecture for surfaces with p_g=0” (folder preprints/Blochs-Conjecture-for-Surfaces-with-pg-equals-q-equals-0-September-24-2026, dated September 24, 2026), filed under the section “Algebraic and complex geometry”. There is no file lean/docs/040.md, and history.md reports no revision of the manuscript. 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 040, section “Algebraic and complex geometry”, 1 manuscript dated Sep 24, 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 40 of 372, by family number
- Not evaluated : The sharp ordinary-double-point volume gap (family 037)
- 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)
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