{"id":"openai-math/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras","pdf":"https://github.com/openai/math/blob/main/preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Quadratic-Strong-Operator-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026","tags":["operator-algebras","von-neumann-algebras","paving-conjecture","functional-analysis"],"score":0,"title":"Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras","domain":"Operator algebras","family":"300","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We prove the quadratic strong-operator paving conjecture of Popa and Vaes. For every $`0\\lt \\varepsilon \\lt 1`$, every self-adjoint element of a von Neumann algebra admits strong-operator paving over each maximal abelian subalgebra with at most $`5\\times10^8\\varepsilon ^{-2}`$ projections. The bound is uniform over representations and requires no separability or conditional-expectation assumption.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Approximation and quadratic strong-operator paving"}