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The Bass trace conjecture for complex group rings of all discrete groups

Theorem 1.1 (24 September): for every discrete group $G$ , every $x\in K_0(\mathbb CG)$ and every infinite-order $g$ , $\mathrm{HS}_G(x)([g])=0$ ; the integral (identity-support) form for $\mathbb ZG$ is deduced in Section 9. The 5 October companion proves the $\ell^1$ -Bass conjecture (BCM 2004, Conjecture 2.2): the trace of every idempotent over $\ell^1(G)$ is supported on finitely many finite-order classes, with no assembly hypothesis, which implies the complex form. Neither manuscript addresses the reduced $C^*$ -algebra (the Kadison-Kaplansky question), where this release separately claims a counterexample.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Bass trace conjecture for complex group rings of all discrete groups · Bass trace conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: The Bass trace conjecture for complex group rings of all discrete groups

specialist registry · passed

No independent mathematician has checked this yet. Checked here: abstracts, introductions and main theorems of both manuscripts (TeX source), read against the Bass conjecture as cited (BCM 2004 Conjecture 2.1; Chatterji-Mislin 2011 Conjecture 2). Lean: Comparator challenge BassTrace, declaration OAI.BassTrace.RightProjective.bassTraceModules_vanishing_and_support (listed in lean/formalization.yaml). Its statement was read here: for every group $G$ and every class $x$ in a module-level $K_0(\mathbb C[G])$ , the Hattori-Stallings trace vanishes at every infinite-order conjugacy class and its support lies in finite-order classes. That is the complex headline. Not rebuilt here. The $\ell^1$ -Bass theorem of the 5 October companion is stronger and is NOT formalized; the manuscript says its proof does not use the complex theorem as input.

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The Bass trace conjecture for complex group rings of all discrete groups

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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The l1-Bass Conjecture for Discrete Groups (companion, stronger l1 form)

paper · pending

paper link supplied by the VibeMathed registry.

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Lean Comparator challenge BassTrace (OpenAI math release)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean Comparator challenge BassTrace (OpenAI math release)

lean artifact · pending

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Compute record

No linked compute attempts recorded.

Lineage and corrections

Lean Comparator challenge BassTrace (OpenAI math release) evidence for this event

This event attributed to Unreleased internal OpenAI model

VibeMathed record: The Bass trace conjecture for complex group rings of all discrete groups evidence for this event

The l1-Bass Conjecture for Discrete Groups (companion, stronger l1 form) evidence for this event

The Bass trace conjecture for complex group rings of all discrete groups evidence for this event

The Bass trace conjecture for complex group rings of all discrete groups parent of this event

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