Not evaluated
Fontaine–Mazur modularity at the prime 2 and 2-adic pro-modularity (family 010)
The gist
In its release of October 6, 2026, OpenAI presents three manuscripts, from an unreleased internal model, on Fontaine-Mazur modularity at the prime 2.
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-010-fontainemazur-modularity-prime-2-2-adic-pro-r1
@misc{discoveria-oai-fam-010-fontainemazur-modularity-prime-2-2-adic-pro-r1,
author = {{DiscoverIA}},
title = {Fontaine–Mazur modularity at the prime 2 and 2-adic pro-modularity (family 010)},
howpublished = {DiscoverIA registry, entry oai-fam-010-fontainemazur-modularity-prime-2-2-adic-pro},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-010-fontainemazur-modularity-prime-2-2-adic-pro#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 their titles, the manuscripts would deal with Fontaine-Mazur modularity (the correspondence between certain representations that describe the symmetries of the solutions of equations, and modular forms) at the prime 2, along with an unrestricted 2-adic "pro-modularity". If the proofs held, this correspondence would be established in that case.
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 give the exact statements, nor 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 · Unrestricted-pro…link only, reading not recorded
- Repositorygithub.com · The-Dimension-of-the-Two…link only, reading not recorded
- Repositorygithub.com · Fontaine-Mazur-modularity…link only, reading not recorded
Method
In the openai/math repository, family 010 gathers three manuscripts: "Unrestricted pro-modularity at the prime two" (October 6, 2026), "The Dimension of the Two-Adic Hecke Algebra at Odd Level" (October 5, 2026) and "Fontaine–Mazur modularity at the prime 2" (October 6, 2026). history.md of October 7, 2026 reports, for the first and the third, an update of citations to revised manuscripts in the collection. The absence of Lean is inferred from the absence of lean/docs/010.md. 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 010, section “Number theory”, 3 manuscripts dated Oct 5, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 4 : 4 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 10 of 372, by family number
- Not evaluated : Two-point Chowla and the corrected binary Elliott conjecture (family 007)
- Not evaluated : The Deligne–Drinfeld conjecture (family 008)
- Not evaluated : Bogomolov–Pop and Milnor K-theoretic reconstruction (family 009)
- Not evaluated : Fontaine–Mazur modularity at the prime 2 and 2-adic pro-modularity (family 010)
- Not evaluated : The Ford–Konyagin–Luca conjecture on prime predecessors (family 011)
- Not evaluated : Independent largest prime factors of consecutive integers (family 012)
- Not evaluated : Ostmann's inverse Goldbach conjecture (family 013)
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