Nuclear ultrapower embedding counterexample

Family 292: Kirchberg's $\mathcal O_2$ norm-ultrapower embedding problem. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Prevent a blanket assumption that a specified separable full group C-star algebra embeds into a norm ultrapower of a fixed nonzero unital nuclear target.

Applicability and commercial boundary

The target, norm ultrapower and free ultrafilter are part of the claim; this is not ordinary database embedding failure.

Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

Next verification action

Extract the explicit group and exact embedding obstruction.

Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

An explicit obstruction to nuclear norm-ultrapower embeddings.