Short··0:21·Operator algebras
Kadison–Ringrose Cohomology Conjecture: Every Twist Is Fake
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About this video
The Kadison–Ringrose conjecture asks whether every bounded Hochschild cocycle on a von Neumann algebra, a consistent "twist" of its multiplication, is just the shadow of a bounded primitive, so that all higher bounded Hochschild cohomology groups vanish. OpenAI claims a proof for every degree at least two, which together with the known degree-one theorem (every derivation is inner) resolves the conjecture; this is OpenAI's preprint, not yet peer reviewed. The animation shows the smallest honest case: a real 2-cocycle on 3×3 matrices (729 numbers, checked on all 729 basis triples) whose computed primitive ψ removes it completely, up to about 2e-15.
Paper (OpenAI, catalogue result 295):
- Vanishing of higher bounded Hochschild cohomology: github.com/openai/math/blob/main/preprints/Vanishing-of-highe…
The animation illustrates the result; it is not a proof.
Gradient Damage: mathematics you can see, equations you can hear.
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Every result explained: gradientdamage.com/p/295
About the problem
Operator algebras·OpenAI Math·Result 295
The Kadison–Ringrose cohomology conjecture
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)
Topics
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