OpenAI · 312-01 · 2026-09-24 · Topology
The Grothendieck homotopy hypothesis via elementary expansions
preprints/The-Grothendieck-homotopy-hypothesis-via-elementary-expansions-September-24-2026
Family 312. The Grothendieck homotopy hypothesis.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves the Grothendieck homotopy hypothesis for -groupoids associated with every Grothendieck coherator in the Ara–Henry convention: these algebraic objects recover the homotopy theory of spaces.
We prove the Grothendieck homotopy hypothesis for every Grothendieck coherator in the Ara–Henry convention: its weak globular infinity-groupoids recover the homotopy theory of spaces. We also resolve Henry's pushout conjecture, showing that elementary expansions preserve components and all homotopy groups of cellular infinity-groupoids.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 312: The Grothendieck homotopy hypothesis. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.