The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n

Theorem 1.1: for every $n\in\{1,2,\dots\}\cup\{\infty\}$ , the classes $W_n=N_n^{-1}(W_{KQ})$ , $F_n=(\mathrm{Ex}^2N_n)^{-1}(\mathrm{Fib}_{KQ})$ and $C_n={}^{\perp}(F_n\cap W_n)$ form a proper combinatorial model structure on small strict $n$ -categories, cofibrantly generated by the images of boundary and horn inclusions under $c_n\mathrm{Sd}^2$ , and $c_n\mathrm{Sd}^2\dashv\mathrm{Ex}^2N_n$ is a Quillen equivalence with Kan-Quillen simplicial sets. The key step proves the Ara-Maltsiniotis pushout condition (Scholie 5.14 (d')). It concerns strict globular categories only, not weak higher categories or n-fold categories.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 25, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n · Ara-Maltsiniotis Thomason conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

Open the source record ↗

Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against the Ara-Maltsiniotis conjecture as recorded by Ara (2023) and Guetta-Maltsiniotis (2024). The Lean challenge lean/ComparatorChallenges/ThomasonModelStructures.json (declarations OAI.Thomason.main and OAI.Thomason.nerveDetection_allDimensions; solution module OAI/CategoryTheory/Thomason/RankedFaithfulness.lean present at the pinned commit) is not in the formalization catalogue. Its top-level statement was read here: for strict omega-categories and for each finite n at least 1 there is a model category whose weak equivalences and fibrations are created by Ex^2 of the Street nerve, with the induced cofibrations, generating sets from boundary and horn images, left and right properness, local presentability and a Quillen equivalence condition; a second statement identifies weak equivalences through the Street nerve. That is the headline. The challenge file is about 136 KB because it defines strict omega-categories and orientals itself; those definitions were not audited. Not rebuilt here.

Source ↗

The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Lean: OAI/CategoryTheory/Thomason/RankedFaithfulness.lean

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

Source ↗

Ara and Maltsiniotis, Vers une structure de categorie de modeles a la Thomason (arXiv 1305.5086)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Lean: OAI/CategoryTheory/Thomason/RankedFaithfulness.lean

lean artifact · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Ara and Maltsiniotis, Vers une structure de categorie de modeles a la Thomason (arXiv 1305.5086) evidence for this event

This event attributed to Unreleased internal OpenAI model

VibeMathed record: The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n evidence for this event

The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n evidence for this event

Lean: OAI/CategoryTheory/Thomason/RankedFaithfulness.lean evidence for this event

The Ara-Maltsiniotis conjecture: Thomason model structures on strict n-categories for every n parent of this event

Act on this frontier

Verify, challenge, or extend the result.

Help verify Open canonical problem Explore evidence graph