lean artifact · pending
Artifact ↗Source authenticated
Grothendieck's homotopy hypothesis for weak globular infinity-groupoids (Ara-Henry coherators)
Theorem 1.1 (Henry's pushout conjecture): for every Grothendieck coherator in the Ara-Henry convention, elementary expansions of cellular models are weak equivalences. Section 5 derives the canonical left semi-model structure and, through Henry's comparison, a Quillen equivalence with spaces, so the homotopy theory is independent of the coherator within that convention. It does not cover coherators outside the Ara-Henry convention, Grothendieck's weak -categories (the non-invertible case), or Taylor's generalized pushout conjecture for algebraic coherators.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. 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: Grothendieck's homotopy hypothesis for weak globular infinity-groupoids (Ara-Henry coherators) · Grothendieck homotopy hypothesis
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Theorem 1.1 (Henry's pushout conjecture): for every Grothendieck coherator in the Ara-Henry convention, elementary expansions of cellular models are weak equivalences. Section 5 derives the canonical left semi-model structure and, through Henry's comparison, a Quillen equivalence with spaces, so the homotopy theory is independent of the coherator within that convention. It does not cover coherators outside the Ara-Henry convention, Grothendieck's weak -categories (the non-invertible case), or Taylor's generalized pushout conjecture for algebraic coherators. parent of this event
Grothendieck's homotopy hypothesis for weak globular infinity-groupoids (Ara-Henry coherators) evidence for this event
Comparator statement: GrothendieckElementaryExpansion.lean evidence for this event
This event attributed to Unreleased internal OpenAI model
Lean proof of Henry's pushout conjecture (OAI.Grothendieck.elementary_expansion) evidence for this event
VibeMathed record: Grothendieck's homotopy hypothesis for weak globular infinity-groupoids (Ara-Henry coherators) evidence for this event
Henry, Algebraic models of homotopy types and the homotopy hypothesis (arXiv 1609.04622) evidence for this event
Grothendieck's homotopy hypothesis for weak globular infinity-groupoids (Ara-Henry coherators) parent of this event
Act on this frontier