Not evaluated
Katok's entropy rigidity conjecture (family 339)
The gist
On October 6, 2026, OpenAI announced a manuscript on entropy equality and local symmetry in negative curvature, linked to Katok's entropy rigidity conjecture.
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-339-katoks-entropy-rigidity-conjecture-r1
@misc{discoveria-oai-fam-339-katoks-entropy-rigidity-conjecture-r1,
author = {{DiscoverIA}},
title = {Katok's entropy rigidity conjecture (family 339)},
howpublished = {DiscoverIA registry, entry oai-fam-339-katoks-entropy-rigidity-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-339-katoks-entropy-rigidity-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
A conjecture is a statement put forward as true, without an accepted proof. If the manuscript were correct, it would bring a new result linked to this conjecture, which the repository files under differential geometry.
What remains unclear
No Lean proof (Lean is 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 manuscript's title does not mention Katok's conjecture: the sources read do not say whether the manuscript claims the whole conjecture or only a neighbouring result.
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 · Entropy-equality-and…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “Entropy equality and local symmetry in negative curvature”, dated September 23, 2026 (family 339, section “Differential geometry” of overview.tex). The absence of Lean is inferred from the absence of a lean/docs/339.md file; OpenAI's README states: “Not all have accompanying Lean formalizations.” history.md reports no revision for the manuscripts of this family. 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
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 (Differential geometry)
- In openai/math
- family 339, section “Differential geometry”, 1 manuscript dated Sep 23, 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 333 of 372, by family number
- Not evaluated : Spectral scalar curvature and codimension-two width (family 336)
- Not evaluated : Cartan–Hadamard isoperimetry and CAT(0) fillings (family 337)
- Not evaluated : Yau's uniformization conjecture (family 338)
- Not evaluated : Katok's entropy rigidity conjecture (family 339)
- Not evaluated : Counterexample to the nearby Lagrangian conjecture (family 340)
- Not evaluated : Donaldson's hypersymplectic deformation conjecture (family 341)
- Not evaluated : Donaldson's tamed-to-compatible conjecture (family 342)
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