Not evaluated
The p-adic section conjecture (family 019)
The gist
On October 6, 2026, OpenAI released a manuscript on the p-adic section conjecture, from an unreleased internal model.
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-019-p-adic-section-conjecture-r1
@misc{discoveria-oai-fam-019-p-adic-section-conjecture-r1,
author = {{DiscoverIA}},
title = {The p-adic section conjecture (family 019)},
howpublished = {DiscoverIA registry, entry oai-fam-019-p-adic-section-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-019-p-adic-section-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The manuscript concerns the p-adic section conjecture, but the sources read do not specify its exact scope. If the manuscript were correct, it would bring a result on this conjecture. It is a number theory statement, according to the repository's “Number theory” section.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. 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 · Etale-covers-with-a…link only, reading not recorded
- Repositorygithub.com · The-p-adic-section…link only, reading not recorded
Method
In the openai/math repository, family 019 comprises two manuscripts: “Étale covers with a prescribed exterior sheet” (September 24, 2026) and “The p-adic section conjecture” (October 6, 2026). There is no file lean/docs/019.md, and OpenAI's README states that not all manuscripts have a Lean formalisation. history.md (October 7, 2026) records for “The p-adic section conjecture” an update of citations to revised manuscripts in the collection. 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 019, section “Number theory”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 3 : 3 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 19 of 372, by family number
- Not evaluated : Zilber–Pink in abelian varieties and the Siegel threefold (family 016)
- Not evaluated : OpenAI claims the irrationality exponent of π is 2 (family 017)
- Not evaluated : The Margulis–Platonov conjecture over global fields (family 018)
- Not evaluated : The p-adic section conjecture (family 019)
- Not evaluated : Squarefree quartics and power-free polynomial values (family 020)
- Not evaluated : A quadratic bound for Jacobsthal's function (family 021)
- Not evaluated : The weak inhomogeneous Duffin–Schaeffer conjecture (family 022)
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