OpenAI · 292-01 · 2026-09-23 · Operator algebras
An explicit obstruction to nuclear norm-ultrapower embeddings
preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026
Family 292. A counterexample to Kirchberg's norm-ultrapower embedding problem.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Constructs an explicit separable unital full group -algebra that cannot embed unitally into the norm ultrapower of any fixed nonzero unital nuclear -algebra, for any free ultrafilter on the natural numbers. Taking the target to be answers Kirchberg's norm-ultrapower embedding problem negatively.
We give a negative answer to Kirchberg's norm-ultrapower embedding problem. We construct an explicit separable unital full group C∗-algebra that admits no unital embedding into Bω, for any nonzero unital nuclear C∗-algebra B and any free ultrafilter ω on ℕ. In particular, it does not embed unitally into .
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 292: Kirchberg's norm-ultrapower embedding problem. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.