Not evaluated
A C¹ counterexample to Shub’s entropy conjecture (family 151)
The gist
In its release of October 6, 2026, OpenAI announces, using an unreleased internal model, a C^1 counterexample to Shub's entropy 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-151-c-1-counterexample-shubs-entropy-conjecture-r1
@misc{discoveria-oai-fam-151-c-1-counterexample-shubs-entropy-conjecture-r1,
author = {{DiscoverIA}},
title = {A C¹ counterexample to Shub’s entropy conjecture (family 151)},
howpublished = {DiscoverIA registry, entry oai-fam-151-c-1-counterexample-shubs-entropy-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-151-c-1-counterexample-shubs-entropy-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
Entropy measures the complexity of how a dynamical system evolves, and the class C^1 denotes a regularity (differentiable, with a continuous derivative). If the counterexample held, Shub's entropy conjecture would not be true in this class.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it as unchecked. No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 151.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 · A-C1-Counterexample-to…link only, reading not recorded
- Lean proofgithub.com · 151.mdpage read word for word
- Lean proofgithub.com · C1EntropyCounterexample.le…link only, reading not recorded
Method
The openai/math repository contains the manuscript “A C^1 Counterexample to the Entropy Conjecture”, dated September 25, 2026, and the file lean/docs/151.md, which describes the Lean formalisation with one Comparator statement (lean/ComparatorChallenges/C1EntropyCounterexample.lean). In formalization.yaml, the family is not among the listed sources; history.md reports no revision of this manuscript. 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 151, section “Dynamical systems and ergodic theory”, 1 manuscript dated Sep 25, 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 147 of 372, by family number
- 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)
- Not evaluated : A C¹ counterexample to Shub’s entropy conjecture (family 151)
- Not evaluated : Zero entropy does not guarantee a smooth positive-volume model (family 152)
- Not evaluated : Arithmetic classification of Bernoulli convolutions (family 153)
- Not evaluated : Pointwise multiple ergodic averages for mixing transformations (family 154)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.