Not evaluated
The near-boundary Birkhoff conjecture (family 147)
The gist
On October 6, 2026, OpenAI announced two manuscripts on caustic collars and the rigidity of smooth billiards, 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-147-near-boundary-birkhoff-conjecture-r1
@misc{discoveria-oai-fam-147-near-boundary-birkhoff-conjecture-r1,
author = {{DiscoverIA}},
title = {The near-boundary Birkhoff conjecture (family 147)},
howpublished = {DiscoverIA registry, entry oai-fam-147-near-boundary-birkhoff-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-147-near-boundary-birkhoff-conjecture#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 manuscripts were correct, they would bring, according to their titles, a result on caustic collars and a rigidity result for smooth billiards with a continuous caustic collar. A billiard is a region in which a ball bounces off the boundary, and a caustic is a curve such that a trajectory tangent to it stays tangent after each bounce.
What remains unclear
No Lean proof (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded. The sources read give only the manuscripts' titles, not their exact statements, nor their link with the Birkhoff conjecture.
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 · Continuous-Phase…link only, reading not recorded
- Repositorygithub.com · Rigidity-of-Smooth…link only, reading not recorded
Method
The openai/math repository contains two manuscripts, both dated September 24, 2026. The manuscripts are titled “Continuous Phase Foliations Create Analytic Caustic Collars” and “Rigidity of Smooth Billiards with a Continuous Caustic Collar”. They are filed under the section “Dynamical systems and ergodic theory” (overview.tex). The file lean/docs/147.md does not exist, and OpenAI's README states that not all manuscripts have a Lean formalisation. history.md reports no revision of these manuscripts. 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 (Dynamical systems and ergodic theory)
- In openai/math
- family 147, section “Dynamical systems and ergodic theory”, 2 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- 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 143 of 372, by family number
- Not evaluated : Banach's simple Lebesgue-spectrum problem (family 144)
- Not evaluated : Rokhlin's multiple-mixing problem (family 145)
- Not evaluated : Sinai's positive-entropy conjecture for the standard map (family 146)
- Not evaluated : The near-boundary Birkhoff conjecture (family 147)
- Not evaluated : The dimension formula for self-similar measures on the line (family 148)
- Not evaluated : Permanence for weakly reversible reaction networks (family 149)
- Not evaluated : Weak mixing of irrational triangular billiards (family 150)
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