Not evaluated
Sinai's positive-entropy conjecture for the standard map (family 146)
The gist
OpenAI presents, in a manuscript announced on October 6, 2026, work on positive metric entropy for the standard map at large parameters.
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-146-sinais-positive-entropy-conjecture-standard-r1
@misc{discoveria-oai-fam-146-sinais-positive-entropy-conjecture-standard-r1,
author = {{DiscoverIA}},
title = {Sinai's positive-entropy conjecture for the standard map (family 146)},
howpublished = {DiscoverIA registry, entry oai-fam-146-sinais-positive-entropy-conjecture-standard},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-146-sinais-positive-entropy-conjecture-standard#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 standard map is a step-by-step rule of evolution with an adjustable parameter; metric entropy measures how fast the uncertainty about the state of the system grows. If the manuscript held, this entropy would be positive at large parameters, which is associated with chaotic behaviour.
What remains unclear
The repository file formalization.yaml marks the Lean (a language in which a computer checks every step of a proof) supplied by OpenAI as “review: status: unchecked”. No third-party check has been read, so it is not known whether the manuscript holds.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 146.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 · Positive-Metric-Entropy…link only, reading not recorded
- Lean proofgithub.com · 146.mdpage read word for word
- Lean proofgithub.com · StandardMapComponents.leanlink only, reading not recorded
- Lean proofgithub.com · StandardMapEntropy.leanlink only, reading not recorded
- Lean proofgithub.com · StandardMapLyapunov.leanlink only, reading not recorded
Method
A manuscript dated September 23, 2026: “Positive Metric Entropy for the Standard Map at Large Parameters”. It is listed in CONTENTS.md and classified under the section “Dynamical systems and ergodic theory” of overview.tex. The repository contains lean/docs/146.md and 3 Comparator statements. 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: “describes the scope of the Lean formalization”).
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 (Dynamical systems and ergodic theory)
- In openai/math
- family 146, section “Dynamical systems and ergodic theory”, 1 manuscript dated Sep 23, 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
- 6 : 1 read word for word, 5 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 142 of 372, by family number
- Not evaluated : Uniform limit-cycle bounds in Hilbert's sixteenth problem (family 143)
- 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)
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