Not evaluated
Rational Hodge conjecture for CM abelian varieties (family 032)
The gist
On October 6, 2026, OpenAI announced, in a manuscript (preprint), a proof of the Hodge conjecture for abelian varieties with complex multiplication (CM).
DiscoverIA status on October 11, 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 11, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 11, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-032-hodge-cm-r1
@misc{discoveria-oai-fam-032-hodge-cm-r1,
author = {{DiscoverIA}},
title = {Rational Hodge conjecture for CM abelian varieties (family 032)},
howpublished = {DiscoverIA registry, entry oai-fam-032-hodge-cm},
note = {Status “Not evaluated”, snapshot 1, recorded on October 11, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-032-hodge-cm#releve-1},
urldate = {2026-10-11}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the proof held, the Hodge conjecture, a conjecture in algebraic geometry, would be established for CM abelian varieties: geometric objects whose points can be added together and which have extra symmetries. The result would concern this family only.
What remains unclear
No verifier is named in the sources read. Three withdrawn manuscripts (Weil, K3) sit next to this one in the repository but are different manuscripts: a dependence link between this family and them is not established in the sources. OpenAI's README flags a procedural exception for this family; its nature is not specified in the sources read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com
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.compage read word for word
Method
The README of the openai/math repository (undated page) describes the release as a “proof of the Hodge Conjecture for CM abelian varieties”. The sources read give neither the manuscript's title nor any information on a Lean formalisation. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 11, 2026 from github.com (page read, quotation checked word for word).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (algebraic geometry)
- Checked by
- no verifier identified
- Sources
- 1 : 1 read word for word
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
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 32 of 372, by family number
- Not evaluated : Artin's primitive root conjecture: infinitude for every base (family 029)
- Not evaluated : Modularity over imaginary quadratic fields (family 030)
- Not evaluated : Uchida's conjecture for open Galois homomorphisms (family 031)
- Not evaluated : Rational Hodge conjecture for CM abelian varieties (family 032)
- Not evaluated : Campana's orbifold Iitaka conjecture and logarithmic subadditivity (family 033)
- Not evaluated : Log abundance and effective Iitaka fibrations (family 034)
- Not evaluated : Threefold log abundance in numerical dimension one in characteristic p>3 (family 035)
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