AI Proof WatchKeep up with AI contributions

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

OpenAI

For every discrete group G, OpenAI claims that the Hattori–Stallings trace of every class in K₀(C G) vanishes on each infinite-order conjugacy class. The claim concerns the complex group ring; an integral identity-only consequence needs a separate known finite-order input.

Sources for this record

What was already known

Bass proved complex vanishing for linear groups, and other work constrained integral finite-order coefficients. Neither covered the stated complex theorem for all discrete groups.

AI involvement AI-led

OpenAI is credited as author and says its internal model produced the mathematical manuscripts and artifacts. No session record establishes stronger autonomy or a named human explanation of this proof.

OpenAI is the credited author and its release attributes mathematical manuscript production to the internal model; session-level independence is unspecified.

Importance Major

Extends the complex Bass trace support theorem to arbitrary discrete groups.

Limitations

The released Lean theorem states vanishing and finite-order support for the projective-module K₀ presentation over C G. The library and dependencies have not had an independent build or statement-correspondence audit, and no named human proof review is documented. The torsion-free idempotent corollary is a separate result.

Technical verification Formal (Lean)

The released Lean solution states vanishing and support for the projective-module K_0 presentation over C G for any group, matching the manuscript's complex trace claim. The comparator configuration names this theorem and permits only standard logical axioms. This is a repository-reported Lean check, not a build reproduced here.

Formal checking

Lean states vanishing on infinite-order conjugacy classes for arbitrary discrete groups.

Checker
Lean solution module OAI.RingTheory.BassTrace.Main
Scope
Hattori–Stallings vanishing on infinite-order conjugacy classes and finite-order support for projective modules over C G, all groups G
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Few

The manuscript explains the proposed mechanism, but no named human explanation is documented; Few is the evidence default.

Correction and publication history