Not evaluated
Deterministic construction of strong thin spanning trees (family 174)
The gist
On October 6, 2026, OpenAI released two manuscripts on the “strong thin tree” conjecture and on constructing trees of this kind.
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-174-deterministic-construction-strong-thin-r1
@misc{discoveria-oai-fam-174-deterministic-construction-strong-thin-r1,
author = {{DiscoverIA}},
title = {Deterministic construction of strong thin spanning trees (family 174)},
howpublished = {DiscoverIA registry, entry oai-fam-174-deterministic-construction-strong-thin},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-174-deterministic-construction-strong-thin#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 held, they would bring a result on that conjecture and a construction method running in polynomial time. Polynomial time means a computing time bounded by a polynomial in the size of the data.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review “unchecked”. No third-party verification is recorded. The manuscripts come from an internal model that OpenAI has not released.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 174.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-strong-thin-tree…link only, reading not recorded
- Repositorygithub.com · A-polynomial-time…link only, reading not recorded
- Lean proofgithub.com · 174.mdpage read word for word
- Lean proofgithub.com · AlgorithmicThinTrees.leanlink only, reading not recorded
- Lean proofgithub.com · StrongThinTree.leanlink only, reading not recorded
Method
In the openai/math release, family 174 has two manuscripts dated September 23, 2026, filed under the section “Combinatorics” of overview.tex. They are “The strong thin tree conjecture” and “A polynomial-time construction of strong thin trees”; history.md reports no revision. OpenAI adds 2 Lean Comparator files, lean/ComparatorChallenges/AlgorithmicThinTrees.lean and lean/ComparatorChallenges/StrongThinTree.lean, described in lean/docs/174.md. 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 (Combinatorics)
- In openai/math
- family 174, section “Combinatorics”, 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
- 6 : 1 read word for word, 5 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 168 of 372, by family number
- Not evaluated : The hypercube Ramsey conjecture (family 171)
- Not evaluated : Classification of finite Euclidean Ramsey configurations (family 172)
- Not evaluated : Seymour's second-neighborhood conjecture (family 173)
- Not evaluated : Deterministic construction of strong thin spanning trees (family 174)
- Not evaluated : Talagrand's conjectures and graph decompositions at expectation thresholds (family 175)
- Not evaluated : The second Kahn–Kalai conjecture (family 176)
- Not evaluated : Bounded-degree coboundary expanders in every dimension (family 177)
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