# Idempotent trace support and coefficient-regime audit

Family 207: The ℓ¹-Bass conjecture for all discrete groups. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algebra formalization researchers can connect trace support conclusions with discrete groups and distinguish characteristic-zero algebraic companions.

## Applicability and commercial boundary

The l1 analytic algebra differs from a finite group ring. Characteristic-zero idempotent conclusions should not be conflated with characteristic-two zero-divisor counterexamples.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

## Next verification action

Build a coefficient/analytic-completion crosswalk and exact finite example.

## Evidence scope

The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The ℓ¹-Bass Conjecture for Discrete Groups](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-l1-Bass-Conjecture-for-Discrete-Groups-October-5-2026/l1-bass-conjecture.pdf).