Not evaluated
The dimension formula for self-similar measures on the line (family 148)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript on the entropy-rate dimension formula for self-similar measures on the line.
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-148-dimension-formula-self-similar-measures-line-r1
@misc{discoveria-oai-fam-148-dimension-formula-self-similar-measures-line-r1,
author = {{DiscoverIA}},
title = {The dimension formula for self-similar measures on the line (family 148)},
howpublished = {DiscoverIA registry, entry oai-fam-148-dimension-formula-self-similar-measures-line},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-148-dimension-formula-self-similar-measures-line#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 give the dimension of self-similar measures on the line, that is, of distributions of mass obtained by copying the measure, scaled down, within itself. The title indicates that the formula involves an entropy rate.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded. The sources read do not state the assumptions of the formula.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 148.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 · The-entropy-rate…link only, reading not recorded
- Lean proofgithub.com · 148.mdpage read word for word
- Lean proofgithub.com · SelfSimilar.leanlink only, reading not recorded
- Lean proofgithub.com · SelfSimilarCorollaries.lea…link only, reading not recorded
Method
The manuscript “The entropy-rate dimension formula for self-similar measures on the line”, dated September 24, 2026, is attributed to an unreleased internal OpenAI model. The file lean/docs/148.md describes the scope of the Lean formalisation, which has 2 Comparator statements (lean/ComparatorChallenges/SelfSimilar.lean and lean/ComparatorChallenges/SelfSimilarCorollaries.lean); the family is among the sources listed in formalization.yaml, and history.md reports no revision of the 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 148, section “Dynamical systems and ergodic theory”, 1 manuscript dated Sep 24, 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
- 5 : 1 read word for word, 4 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 144 of 372, by family number
- 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)
- Not evaluated : Weak mixing of irrational triangular billiards (family 150)
- Not evaluated : A C¹ counterexample to Shub’s entropy conjecture (family 151)
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