# Quasitrace and tensor-finiteness counterexample

Family 294: Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record nonadditive normalized two-quasitraces and the specified finite-algebra tensor product becoming properly infinite.

## Applicability and commercial boundary

Quasitraces differ from ordinary additive traces; abstract C-star tensor products differ from finite numeric Kronecker products.

## 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 precise algebras, tensor norm and quasitrace witnesses.

## 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).

[A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-counterexample-to-Kaplanskys-quasitrace-conjecture-September-23-2026/paper.pdf).