Not evaluated
The geometric case of the Erdős similarity conjecture (family 084)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, two manuscripts on the Erdős similarity conjecture, geometric and dyadic cases, 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-084-geometric-case-erdos-similarity-conjecture-r1
@misc{discoveria-oai-fam-084-geometric-case-erdos-similarity-conjecture-r1,
author = {{DiscoverIA}},
title = {The geometric case of the Erdős similarity conjecture (family 084)},
howpublished = {DiscoverIA registry, entry oai-fam-084-geometric-case-erdos-similarity-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-084-geometric-case-erdos-similarity-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
If the manuscripts were correct, one of them would establish the geometric case of the Erdős similarity conjecture. This would be one case of the conjecture, not the whole conjecture; a second manuscript in the family treats the dyadic case.
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 no third-party verification is recorded. The repository does not present it as checked, and the sources read do not say which parts of the manuscripts it covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 084.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-geometric-case-of-the…link only, reading not recorded
- Repositorygithub.com · The-dyadic-case-of-the…link only, reading not recorded
- Lean proofgithub.com · 084.mdpage read word for word
- Lean proofgithub.com · DyadicAvoidance.leanlink only, reading not recorded
Method
In the openai/math repository, family 084 comprises two manuscripts: “The geometric case of the Erdős similarity conjecture” (October 5, 2026) and “The dyadic case of the Erdős similarity conjecture” (September 25, 2026). The file lean/docs/084.md describes the scope of the formalisation, with one Comparator statement (lean/ComparatorChallenges/DyadicAvoidance.lean). In formalization.yaml, the review reads “review: status: unchecked” and the family is not among the sources; history.md reports no revision of these manuscripts. 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 (Real and complex analysis)
- In openai/math
- family 084, section “Real and complex analysis”, 2 manuscripts 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
- 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 81 of 372, by family number
- Not evaluated : The David–Semmes Riesz-transform problem in higher codimension (family 081)
- Not evaluated : Maximal and variational bounds for the triangular Hilbert transform (family 082)
- Not evaluated : Stein's conjecture for Hilbert transforms along Lipschitz directions (family 083)
- Not evaluated : The geometric case of the Erdős similarity conjecture (family 084)
- Not evaluated : Endpoint regularity of the planar centered maximal function (family 085)
- Not evaluated : An L³ bound for the trilinear Hilbert transform (family 086)
- Not evaluated : The Mahler conjectures and symplectic width (family 087)
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