Not evaluated
Modularity over imaginary quadratic fields (family 030)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on the modularity of elliptic curves over imaginary quadratic fields.
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-030-modularity-imaginary-quadratic-fields-r1
@misc{discoveria-oai-fam-030-modularity-imaginary-quadratic-fields-r1,
author = {{DiscoverIA}},
title = {Modularity over imaginary quadratic fields (family 030)},
howpublished = {DiscoverIA registry, entry oai-fam-030-modularity-imaginary-quadratic-fields},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-030-modularity-imaginary-quadratic-fields#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 manuscript were correct, it would establish, going by its title, the modularity of elliptic curves (curves given by a cubic equation) over imaginary quadratic fields, that is the rational numbers with the square root of a negative integer added. Modularity links a curve to an object of another kind, a modular form in the broad sense.
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 specify the exact scope of the result, for instance whether it covers all elliptic curves over these fields or only some.
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 · Modularity-of-elliptic…link only, reading not recorded
Method
The manuscript in the openai/math repository is titled “Modularity of elliptic curves over imaginary quadratic fields” and is dated October 4, 2026. The repository has no lean/docs/030.md page, and OpenAI's README states “Not all have accompanying Lean formalizations.”; 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).
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 (Number theory)
- In openai/math
- family 030, section “Number theory”, 1 manuscript dated Oct 4, 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 30 of 372, by family number
- Not evaluated : Integral density on curve character varieties (family 027)
- Not evaluated : The Gaussian moat conjecture (family 028)
- 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)
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