Not evaluated
Zero entropy does not guarantee a smooth positive-volume model (family 152)
The gist
On October 6, 2026, OpenAI released a manuscript claiming a zero-entropy system without a smooth positive-volume 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-152-zero-entropy-does-not-guarantee-smooth-r1
@misc{discoveria-oai-fam-152-zero-entropy-does-not-guarantee-smooth-r1,
author = {{DiscoverIA}},
title = {Zero entropy does not guarantee a smooth positive-volume model (family 152)},
howpublished = {DiscoverIA registry, entry oai-fam-152-zero-entropy-does-not-guarantee-smooth},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-152-zero-entropy-does-not-guarantee-smooth#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A zero-entropy system is one whose entropy, which measures how unpredictable its evolution is, equals zero. A smooth positive-volume model would be a realisation of the system on a regular space equipped with a volume. If the manuscript held, zero entropy would not be enough to guarantee the existence of such a model.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review “unchecked”. No third-party verification is recorded. The manuscript comes from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 152.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-finite-entropy-system…link only, reading not recorded
- Lean proofgithub.com · 152.mdpage read word for word
- Lean proofgithub.com · SmoothObstruction.leanlink only, reading not recorded
Method
In the openai/math release, family 152 has a single manuscript, “A zero-entropy system without a smooth positive-volume model”, dated September 25, 2026. The repository folder is named “A-finite-entropy-system-without-a-smooth-positive-volume-model-September-25-2026”, with “finite-entropy” where the title says “zero-entropy”. OpenAI adds a Lean Comparator file, lean/ComparatorChallenges/SmoothObstruction.lean (1 statement), described in lean/docs/152.md; 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: “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 152, 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 148 of 372, by family number
- 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)
- Not evaluated : A counterexample to periodic tiling in dimension three (family 155)
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