Not evaluated
The factor-of-IID threshold for free Ising states on trees (family 236)
The gist
OpenAI claims, in an announcement of October 6, 2026, a result on the factor-of-IID threshold for the free Ising model on regular trees.
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-236-factor-iid-threshold-free-ising-states-trees-r1
@misc{discoveria-oai-fam-236-factor-iid-threshold-free-ising-states-trees-r1,
author = {{DiscoverIA}},
title = {The factor-of-IID threshold for free Ising states on trees (family 236)},
howpublished = {DiscoverIA registry, entry oai-fam-236-factor-iid-threshold-free-ising-states-trees},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-236-factor-iid-threshold-free-ising-states-trees#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 40 s reading time, estimated
What it changes
If the manuscript held, it would pin down a threshold, in the sense of its title, for the free state of the Ising model on regular trees, relating to the factor-of-IID property. A random state is a factor-of-IID if it is obtained by applying the same rule everywhere to independent, identically distributed random variables attached to the vertices. The Ising model places on each vertex of a graph a spin with two possible values, interacting with its neighbours; a tree is regular when all its vertices have the same number of neighbours.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by the claimant and marked “review: status: unchecked” in formalization.yaml. No third-party check has been read. It is not known which parameter the threshold depends on, nor in which direction it applies.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 236.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-sharp-factor-of-IID…link only, reading not recorded
- Lean proofgithub.com · 236.mdpage read word for word
- Lean proofgithub.com · FreeIsing.leanlink only, reading not recorded
Method
One manuscript, “The sharp factor-of-IID threshold for the free Ising model on regular trees”, dated September 26, 2026. A Comparator statement is described in lean/docs/236.md, with the file lean/ComparatorChallenges/FreeIsing.lean. The family is present in 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 236, section “Probability and statistical mechanics”, 1 manuscript dated Sep 26, 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
- 4 : 1 read word for word, 3 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 230 of 372, by family number
- Not evaluated : The joint critical Ashkin–Teller scaling limit (family 233)
- Not evaluated : All-temperature pressure for orthogonally invariant Ising spin glasses (family 234)
- Not evaluated : Random-SAT thresholds, sharp variance and computability (family 235)
- Not evaluated : The factor-of-IID threshold for free Ising states on trees (family 236)
- Not evaluated : The three-quarter diameter exponent for honeycomb walks (family 237)
- Not evaluated : Optimal logarithmic mixing of the Thorp shuffle (family 238)
- Not evaluated : Sharp singularity rates for symmetric sign matrices (family 239)
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