Operator algebras·OpenAI Math·Result 295·Lean formalisation listed
The Kadison–Ringrose cohomology conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under operator algebras: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
In one line: OpenAI reports a proof of the Kadison–Ringrose cohomology conjecture (operator algebras) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Kadison–Ringrose Cohomology Conjecture: Every Twist Is Fake, is on YouTube.
What OpenAI claims
Proves that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with coefficients in the algebra itself, has a bounded primitive. Equivalently, all higher bounded Hochschild cohomology groups vanish, resolving the Kadison–Ringrose conjecture. (Lean)
Paper
Vanishing of higher bounded Hochschild cohomology
OpenAI's abstract We prove that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with values in the algebra itself, has a bounded primitive. Together with the established degree-one inner-derivation theorem, this resolves the Kadison–Ringrose cohomology conjecture positively.
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 OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.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 that every bounded Hochschild cocycle of degree at least two on a complex von Neumann algebra, with coefficients in the algebra itself, has a bounded primitive. Equivalently, all higher bounded Hochschild cohomology groups vanish, resolving the Kadison–Ringrose conjecture. (Lean)
- Where is the proof?
- In the paper, Vanishing of higher bounded Hochschild cohomology (PDF).
- Is there a video?
- Yes, on YouTube (0:21).
Also in
- Chapter 15 of 83 in Every OpenAI Math Result, Part 1 of 4: Goldfeld's Conjecture and 82 More · starts at 4:54 · watch from there on YouTube →
The video
Kadison–Ringrose Cohomology Conjecture: Every Twist Is Fake · Short · 0:21 · description, sources and transcript →
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