The ℓ¹-Bass conjecture for all discrete groups

What OpenAI claims

Proves the ℓ1-Bass conjecture for every discrete group: Hattori–Stallings traces of idempotent matrices over ℓ¹(G) are supported on finitely many finite-order conjugacy classes. The algebraic companion proves the integral Bass trace conjecture and Kaplansky's idempotent conjecture for torsion-free groups over every commutative unital characteristic-zero domain. (Lean)

Papers (2)

1. The ℓ¹-Bass Conjecture for Discrete Groups

   5 October 2026 · Preprint, not peer reviewed · PDF

   We prove the ℓ1-Bass conjecture for every discrete group. The Hattori–Stallings trace of every idempotent matrix over the complex ℓ1 group algebra is supported on finitely many conjugacy classes of finite-order elements.

2. The Bass trace conjecture and the characteristic-zero Kaplansky idempotent conjecture

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove the complex group-ring Bass trace conjecture for every discrete group: the Hattori–Stallings trace of a finitely generated projective module over its complex group ring is supported on conjugacy classes of finite-order elements. As a consequence, for every torsion-free group G and every commutative unital domain R of characteristic zero, the only idempotents in RG are 0 and 1. This proves Kaplansky's idempotent conjecture in characteristic zero.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.