Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 197-03. A Counterexample to the Group-Ring Determinant Conjecture
Manuscript map · lines 5925–5934
OpenAI@2026-10-07#rem:oai-p-197-03
Authors: OpenAI. Family 197.
Title: A Counterexample to the Group-Ring Determinant Conjecture.
Abstract: We disprove the unrestricted group-ring Determinant Conjecture. We construct a finitely generated group G and a square matrix over ${}mathbb Z[G]$ that is invertible over ${}mathbb Q[G]$ and has Fuglede–Kadison determinant strictly between zero and one. The logarithmic integral defining the determinant is finite.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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