Not evaluated
The critical dimension for the one-phase Bernoulli problem (family 367)
The gist
On October 6, 2026, OpenAI published a manuscript on the critical dimension for one-phase Bernoulli minimizers, 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-367-critical-dimension-one-phase-bernoulli-r1
@misc{discoveria-oai-fam-367-critical-dimension-one-phase-bernoulli-r1,
author = {{DiscoverIA}},
title = {The critical dimension for the one-phase Bernoulli problem (family 367)},
howpublished = {DiscoverIA registry, entry oai-fam-367-critical-dimension-one-phase-bernoulli},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-367-critical-dimension-one-phase-bernoulli#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
This manuscript belongs to partial differential equations (section “Partial differential equations” of overview.tex). If the manuscript were correct, it would provide a result on the critical dimension of this problem.
What remains unclear
The sources read do not state the manuscript's result. The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI and has not been verified by a third party: the repository records it as “review: status: unchecked”. The sources read report no third-party assessment of the manuscript.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 367.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 · The-critical-dimension…link only, reading not recorded
- Lean proofgithub.com · 367.mdpage read word for word
- Lean proofgithub.com · BernoulliNonflatInSeven.le…link only, reading not recorded
Method
The manuscript “The critical dimension for one-phase Bernoulli minimizers”, dated September 24, 2026, is listed in CONTENTS.md of the openai/math repository. The repository supplies lean/docs/367.md, which “describes the scope of the Lean formalization”, and one Comparator statement: lean/ComparatorChallenges/BernoulliNonflatInSeven.lean. The family is absent from the `sources` of formalization.yaml. 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).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Partial differential equations)
- In openai/math
- family 367, section “Partial differential equations”, 1 manuscript dated Sep 24, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 360 of 372, by family number
- Not evaluated : Kinetic limits and fluctuations over the Boltzmann lifespan (family 364)
- Not evaluated : Joint metric and connection recovery from one boundary patch (family 365)
- Not evaluated : The planar Mumford–Shah regularity conjecture (family 366)
- Not evaluated : The critical dimension for the one-phase Bernoulli problem (family 367)
- Not evaluated : The three-dimensional Ball–Evans approximation problem (family 368)
- Not evaluated : The hot spots conjecture for simply connected planar domains (family 369)
- Not evaluated : The subcritical Lane–Emden and Hénon–Lane–Emden conjectures (family 370)
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