# Assembly and projection counterexample ledger

Family 285: Counterexamples to Baum–Connes and Kadison–Kaplansky. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track rational injectivity/surjectivity failures of the specified Baum–Connes assembly map and a torsion-free reduced-C-star projection example.

## Applicability and commercial boundary

These infinite operator-algebra statements do not imply ordinary finite matrices lose injectivity or have unexpected projections.

## 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

Separate the companion claims and extract exact group/assembly data.

## 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 torsion-free counterexample to reduced Baum–Connes injectivity](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Torsion-Free-Counterexample-to-Reduced-Baum-Connes-Injectivity-September-23-2026/paper.pdf).