Breakthrough Tracker record
An explicit Heisenberg-group element is claimed to refute determinant approximation
Kammeyer gives the element 1−2a+2b in the integral group ring of the discrete Heisenberg group, with infinite Fuglede–Kadison determinant 2 while finite-quotient determinants have limsup at most the cube root of 5.
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- Stable ID
math-determinant-approximation-counterexample-2026- Revision
math-determinant-approximation-counterexample-2026.v1- Field
- Mathematics · Operator algebras, group theory and L² invariants
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Provisional explicit counterexample
- Last checked
AI role
ChatGPT 6 Astra Pro recognized the relevance of Jan Boschheidgen’s theorem after a detailed prompt. Kammeyer says he wrote and verified the paper and credits Boschheidgen for the underlying input.
Record details
- Problem or result
- Determinant approximation for finite quotients of residually finite groups
- Authors
- Holger Kammeyer
- Institutions
- Heinrich Heine University Düsseldorf
- Result date
- First-version preprint submitted September 14, 2026
Why it matters
The example would refute a standing approximation conjecture in a simple class-two nilpotent setting and block a proposed L²-torsion approximation route.
Limits
This is a primary-only, non-peer-reviewed preprint. No independent correctness assessment was located.
Sources
Correction and revision history
- 2026-10-02 — Added after primary-source, scope, status, AI-role and limitation review.
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