Not evaluated
Uchida's conjecture for open Galois homomorphisms (family 031)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript, from an unreleased internal model, on Uchida's conjecture for open Galois homomorphisms.
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-031-uchidas-conjecture-open-galois-homomorphisms-r1
@misc{discoveria-oai-fam-031-uchidas-conjecture-open-galois-homomorphisms-r1,
author = {{DiscoverIA}},
title = {Uchida's conjecture for open Galois homomorphisms (family 031)},
howpublished = {DiscoverIA registry, entry oai-fam-031-uchidas-conjecture-open-galois-homomorphisms},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-031-uchidas-conjecture-open-galois-homomorphisms#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
According to the family's title, the manuscript would deal with Uchida's conjecture for open homomorphisms, that is, correspondences between Galois groups of a certain type. If the manuscript were correct, it would bring a result on this conjecture; the sources read do not specify its exact scope.
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 · Open-Homomorphisms-of…link only, reading not recorded
Method
The openai/math repository attaches a single manuscript to family 031, "Open Homomorphisms of Global Solvably Closed Galois Groups", dated October 5, 2026. The absence of Lean is inferred from the absence of lean/docs/031.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 (Number theory)
- In openai/math
- family 031, section “Number theory”, 1 manuscript dated Oct 5, 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 31 of 372, by family number
- 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)
- Not evaluated : Log abundance and effective Iitaka fibrations (family 034)
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