Not evaluated
The free uniform spanning forest is a factor of IID (family 231)
The gist
In its release of October 6, 2026, OpenAI claims that the free uniform spanning forest is a factor of IID (manuscript dated September 25, 2026).
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-231-free-uniform-spanning-forest-factor-iid-r1
@misc{discoveria-oai-fam-231-free-uniform-spanning-forest-factor-iid-r1,
author = {{DiscoverIA}},
title = {The free uniform spanning forest is a factor of IID (family 231)},
howpublished = {DiscoverIA registry, entry oai-fam-231-free-uniform-spanning-forest-factor-iid},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-231-free-uniform-spanning-forest-factor-iid#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 held, this forest (a subgraph with no cycle containing all the vertices) would be obtained from IID random variables (independent and identically distributed). The rule would have to respect the graph's symmetries. The subject belongs to probability and statistical mechanics.
What remains unclear
No third party is recorded as a checker, and the Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, marked “unchecked”. The sources read do not state on which graph or in what setting the manuscript would establish this result.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 231.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-free-uniform-spanning…link only, reading not recorded
- Lean proofgithub.com · 231.mdpage read word for word
- Lean proofgithub.com · FreeUniformSpanningForest.…link only, reading not recorded
- Lean proofgithub.com · StronglyRayleighDPP.leanlink only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “The free uniform spanning forest is a factor of IID”, dated September 25, 2026, the only one of family 231. Lean supplied: lean/docs/231.md, lean/ComparatorChallenges/FreeUniformSpanningForest.lean and lean/ComparatorChallenges/StronglyRayleighDPP.lean (2 Comparator statements). The family is absent from 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 (Probability and statistical mechanics)
- In openai/math
- family 231, section “Probability and statistical mechanics”, 1 manuscript 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 225 of 372, by family number
- Not evaluated : Continuum phase transitions for radial pair potentials (family 228)
- Not evaluated : Sharp three- and four-state reconstruction thresholds (family 229)
- Not evaluated : Exact Hausdorff measure for SLE (family 230)
- Not evaluated : The free uniform spanning forest is a factor of IID (family 231)
- Not evaluated : Gaussian fields and SLE interfaces for Lipschitz heights (family 232)
- Not evaluated : The joint critical Ashkin–Teller scaling limit (family 233)
- Not evaluated : All-temperature pressure for orthogonally invariant Ising spin glasses (family 234)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.