# 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](source.json).

[An explicit obstruction to nuclear norm-ultrapower embeddings](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-obstruction-to-nuclear-norm-ultrapower-embeddings-September-23-2026/paper.pdf).