Topology·OpenAI Math·Result 312·Lean formalisation listed
The Grothendieck homotopy hypothesis
One of the 372 results in OpenAI's public mathematics catalogue, filed under topology: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
Also known as Grothendieck's homotopy hypothesis; homotopy hypothesis
In one line: OpenAI reports a proof of the Grothendieck homotopy hypothesis (topology) in a preprint dated 24 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More, is on YouTube.
Chapter 18 of 84 in Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · starts at 5:57 · watch from there on YouTube →
What OpenAI claims
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. (Lean)
Paper
The Grothendieck homotopy hypothesis via elementary expansions
OpenAI's abstract 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.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 24 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- 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. (Lean)
- Where is the proof?
- In the paper, The Grothendieck homotopy hypothesis via elementary expansions (PDF).
- Is there a video?
- Yes, on YouTube (29:20, chapter 18).
Also in
- Chapter 7 of 10 in Kervaire Invariant Problem at Prime 3, The Grothendieck Homotopy Hypothesis and 8 More · starts at 2:06 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 3 of 4: Operator Paving, Naimark's Problem and 82 More · Compilation · 29:20 · chapter 18 from 5:57 · description, sources and chapters →
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