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.

A torsion-free counterexample to reduced Baum–Connes injectivity.