Not evaluated
Banach's simple Lebesgue-spectrum problem (family 144)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript on a smooth three-torus diffeomorphism with simple Lebesgue spectrum, with a Lean file.
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-144-banachs-simple-lebesgue-spectrum-problem-r1
@misc{discoveria-oai-fam-144-banachs-simple-lebesgue-spectrum-problem-r1,
author = {{DiscoverIA}},
title = {Banach's simple Lebesgue-spectrum problem (family 144)},
howpublished = {DiscoverIA registry, entry oai-fam-144-banachs-simple-lebesgue-spectrum-problem},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-144-banachs-simple-lebesgue-spectrum-problem#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the manuscript were correct, it would provide, according to its title, a diffeomorphism (a smooth, reversible deformation) of the three-dimensional torus with simple Lebesgue spectrum. The family is named “Banach's simple Lebesgue-spectrum problem”.
What remains unclear
The Lean file (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI itself, and the repository marks it “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 · 144.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-smooth-three-torus…link only, reading not recorded
- Lean proofgithub.com · 144.mdpage read word for word
- Lean proofgithub.com · ThreeTorus.leanlink only, reading not recorded
Method
The manuscript “A smooth three-torus diffeomorphism with simple Lebesgue spectrum” makes up family 144. It is dated September 23, 2026 and filed under the section “Dynamical systems and ergodic theory” of overview.tex. The file lean/docs/144.md describes the scope of the formalisation, with one Comparator statement (lean/ComparatorChallenges/ThreeTorus.lean). The family is not among the sources of formalization.yaml; 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 144, 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
- 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 140 of 372, by family number
- Not evaluated : The existential theory of the reals and existential–universal sentences in the counting hierarchy (family 141)
- Not evaluated : Deterministic polynomial factorization over prime fields (family 142)
- 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)
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