{"id":"openai-math/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy","pdf":"https://github.com/openai/math/blob/main/preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Close-Separable-Cstar-Algebras-Without-Spatial-Conjugacy-October-5-2026","tags":["operator-algebras","c-star-algebras","kadison-kastler"],"score":0,"title":"Close Separable C*-Algebras Without Spatial Conjugacy","domain":"Operator algebras","family":"289","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We disprove the separable C ∗ -algebraic spatial form of the Kadison–Kastler conjecture. For every ε > 0, we construct unital, norm-separable C ∗ -algebras on a common separable complex Hilbert space, with the same identity and Kadison–Kastler distance less than ε , that are not conjugate by any unitary. The two algebras have the same von Neumann closure.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Strong Kadison–Kastler stability and its spatial boundaries"}