Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 151. A C 1 counterexample to Shub’s entropy conjecture
Family claims › Dynamical systems and ergodic theory · lines 1074–1079
OpenAI@2026-10-07#rem:oai-151
Constructs a noninvertible self-map of a compact smooth manifold with zero topological entropy but eigenvalue on second homology. This disproves the homological entropy lower bound for general self-maps: homological growth need not force positive orbit complexity.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 143. Uniform limit-cycle bounds in Hilbert's sixteenth problem
- remark: Remark: Family 144. Banach's simple Lebesgue-spectrum problem
- remark: Remark: Family 145. Rokhlin's multiple-mixing problem
- remark: Remark: Family 146. Sinai's positive-entropy conjecture for the standard map
- remark: Remark: Family 147. The near-boundary Birkhoff conjecture
- remark: Remark: Family 148. The dimension formula for self-similar measures on the line
- remark: Remark: Family 149. Permanence for weakly reversible reaction networks
- remark: Remark: Family 150. Weak mixing of irrational triangular billiards