Not evaluated
Arithmetic classification of Bernoulli convolutions (family 153)
The gist
On October 6, 2026, OpenAI announced, with an unreleased internal model, a manuscript on an arithmetic classification and a non-Pisot singularity for Bernoulli convolutions.
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-153-arithmetic-classification-bernoulli-r1
@misc{discoveria-oai-fam-153-arithmetic-classification-bernoulli-r1,
author = {{DiscoverIA}},
title = {Arithmetic classification of Bernoulli convolutions (family 153)},
howpublished = {DiscoverIA registry, entry oai-fam-153-arithmetic-classification-bernoulli},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-153-arithmetic-classification-bernoulli#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 Bernoulli convolution is the law of an infinite sum of successive powers of a fixed number smaller than 1, each given a plus or minus sign drawn at random. If the manuscript held, it would bring an arithmetic classification of these laws and a singularity result called “non-Pisot”. A Pisot number is an algebraic integer greater than 1 whose other conjugates have modulus less than 1.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The title of the manuscript says neither what is classified nor for which parameters the singularity would be obtained.
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 · Arithmetic-classification…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “Arithmetic classification and non-Pisot singularity for Bernoulli convolutions”, dated October 3, 2026. The absence of Lean is inferred from the absence of a lean/docs/153.md file; OpenAI's README states that not all manuscripts have a Lean formalisation. 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: “Not all have accompanying Lean formalizations.”).
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 (Dynamical systems and ergodic theory)
- In openai/math
- family 153, section “Dynamical systems and ergodic theory”, 1 manuscript dated Oct 3, 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 149 of 372, by family number
- 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)
- Not evaluated : Borsuk's conjecture fails in dimension nine (family 156)
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