Not evaluated
Koebe's circle-domain conjecture and circle-domain rigidity (family 071)
The gist
On October 6, 2026, OpenAI released two manuscripts, from an unreleased internal model, on Koebe's circle-domain conjecture and the rigidity of circle domains.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
Text written by an AI, reviewed by Antoine Olivier,
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-071-koebes-circle-domain-conjecture-circle-r1
@misc{discoveria-oai-fam-071-koebes-circle-domain-conjecture-circle-r1,
author = {{DiscoverIA}},
title = {Koebe's circle-domain conjecture and circle-domain rigidity (family 071)},
howpublished = {DiscoverIA registry, entry oai-fam-071-koebes-circle-domain-conjecture-circle},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-071-koebes-circle-domain-conjecture-circle#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 circle domain is a region of the plane whose every boundary is a circle or a point. If the manuscripts held up, they would bring results on Koebe's conjecture, which concerns transforming a region into such a domain by a conformal map (one that preserves angles), and on the rigidity of these domains.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI, and the repository itself marks it "unchecked"; no third-party verification has been read. The sources read do not say exactly what each manuscript establishes.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 071.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 · Removable-Boundaries-and…link only, reading not recorded
- Repositorygithub.com · Koebes-Circle-Domain…link only, reading not recorded
- Lean proofgithub.com · 071.mdpage read word for word
- Lean proofgithub.com · KoebeCircleDomains.leanlink only, reading not recorded
Method
The 071 family of the openai/math release (section "Real and complex analysis") has two manuscripts dated September 23, 2026: "Removable Boundaries and Rigidity of Circle Domains" and "Koebe's Circle-Domain Conjecture". OpenAI adds a Lean file (KoebeCircleDomains.lean, 1 Comparator statement); the repository's history flags no revision of this family's 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 071, section “Real and complex analysis”, 2 manuscripts 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
- 5 : 1 read word for word, 4 links only
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
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 68 of 372, by family number
- Not evaluated : The Campana–Peternell conjecture in dimension six (family 067)
- Not evaluated : Anticanonical nonvanishing under smooth semipositivity (family 068)
- Not evaluated : Quantum geometric Langlands at irrational level (family 069)
- Not evaluated : Koebe's circle-domain conjecture and circle-domain rigidity (family 071)
- Not evaluated : Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
- Not evaluated : The Falconer distance conjecture (family 073)
- Not evaluated : Kakeya in three and four dimensions (family 074)
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