{"id":"palomar/PALOMAR-2026-09-14-000008","url":"https://github.com/SauersML/group-approximation/tree/a4eea122897265caab10088c303451049bdd797f","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-14-000008-v1.json","repo":"https://github.com/SauersML/group-approximation","tags":["math.OA","msc:46L05","msc:46L30","operator-algebras","lean","tracial-completions"],"score":0,"title":"A Counterexample to the Trace Problem for Uniform Tracial Completions","trust":"high","domain":"math.OA","source":"palomar","authors":["Sauers"],"reviews":0,"subject":"math.OA","summary":"We formalize a negative answer to Problem XXII of Schafhauser, Tikuisis and White. There is a separable unital C*-algebra A with nonempty compact tracial state space such that its uniform tracial completion M has a tracial state that is discontinuous in the uniform 2-norm. Thus the canonical extensions of the traces of A form a proper subset X of the traces of M. A second theorem gives a factorial tracially complete pair (M, X) with the same failure, answering Question 1.1 of Carrion, Castillejos, Evington, Gabe, Schafhauser, Tikuisis and White negatively. In both statements, X is exactly…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-14","reactions":{},"formalized":true}