Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 151-01. A C 1 Counterexample to the Entropy Conjecture
Manuscript map · lines 5295–5304
OpenAI@2026-10-07#rem:oai-p-151-01
Authors: OpenAI. Family 151.
Title: A C{}1 Counterexample to the Entropy Conjecture.
Abstract: We disprove the general C1 self-map formulation of Shub's entropy conjecture. We construct a noninvertible C1 self-map of a compact smooth manifold without boundary whose topological entropy is zero, while its action on second real homology has eigenvalue 2. Thus the topological entropy is strictly smaller than the logarithm of the homological spectral radius.
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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