What was already known
The scalar idempotent conjecture remained open for general torsion-free groups in characteristic zero. Earlier group-specific and faithful-trace arguments did not give the all-group Bass support theorem used here.
AI involvement
OpenAI credits its internal model with the mathematical manuscript and Lean development. Earlier faithful-trace methods are human inputs; no named human check or explanation of this corollary is documented.
OpenAI is credited author of the model-produced Bass family; the record does not establish autonomous session conditions.
Importance
This settles the characteristic-zero scalar idempotent conjecture for all torsion-free groups.
Limitations
The corollary depends on the complex Bass theorem. Its Lean proof is repository reported; the build and dependencies have not been independently audited. The statement does not cover positive characteristic, reduced C*-algebras or arbitrary matrix idempotents.
Technical verification
The released Lean TorsionFree solution states that scalar idempotents over every commutative characteristic-zero domain and torsion-free group are trivial, alongside trace-rank assertions. This relies on the formal Bass trace theorem. The check is repository-reported and not reproduced here.
Formal checking
Lean formalization of torsion_free_corollary and domain_idempotent using the Bass support theorem
- Checker
- Lean solution module OAI.RingTheory.BassTrace.TorsionFree
- Scope
- Characteristic-zero scalar idempotents over R G for all torsion-free G and commutative domains R, plus algebraic trace-rank consequences
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The manuscript gives a derivation, but no named human explanation is documented; Few is the evidence default.
Correction and publication history
A distinct scalar-idempotent corollary of the Bass theorem for torsion-free groups.
Read this published revision