Not evaluated
Sharp three- and four-state reconstruction thresholds (family 229)
The gist
In its release of October 6, 2026, OpenAI announces three manuscripts on reconstruction thresholds: two on the four-state Potts model and one on a three-state symmetric channel.
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-229-sharp-three-four-state-reconstruction-r1
@misc{discoveria-oai-fam-229-sharp-three-four-state-reconstruction-r1,
author = {{DiscoverIA}},
title = {Sharp three- and four-state reconstruction thresholds (family 229)},
howpublished = {DiscoverIA registry, entry oai-fam-229-sharp-three-four-state-reconstruction},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-229-sharp-three-four-state-reconstruction#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 reconstruction threshold is the value of the parameter that separates the cases where the state of the tree's root remains guessable from those where it no longer does. If the manuscripts held, this threshold would be known for the ferromagnetic four-state Potts model (each site takes one of four states), and exact for the three-state symmetric channel.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it as unchecked. No third-party verification is recorded. The sources read do not say which manuscripts the Lean statements cover.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 229.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-Reconstruction…link only, reading not recorded
- Repositorygithub.com · A-Capacity-Criterion-for…link only, reading not recorded
- Repositorygithub.com · The-exact-reconstruction…link only, reading not recorded
- Lean proofgithub.com · 229.mdpage read word for word
- Lean proofgithub.com · ThreeStateSupercritical.le…link only, reading not recorded
- Lean proofgithub.com · ThreeStateTreeClauses.leanlink only, reading not recorded
Method
The openai/math repository contains three manuscripts: “The exact reconstruction threshold for the three-state symmetric channel” (September 25, 2026) and two on the Potts model (October 5, 2026). These last two are titled “The Reconstruction Threshold for the Ferromagnetic Four-State Potts Model” and “A Capacity Criterion for Four-State Potts Reconstruction on Trees”. The file lean/docs/229.md describes the Lean formalisation (2 Comparator statements); the family is not listed among the sources of formalization.yaml, and 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 229, section “Probability and statistical mechanics”, 3 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
- 7 : 1 read word for word, 6 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 223 of 372, by family number
- Not evaluated : The double-dimer CLE_4 conjecture in the half-plane (family 226)
- Not evaluated : The dynamical phase transition in the Sherrington–Kirkpatrick model (family 227)
- 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)
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