On this page
Dynamical entropy counterexample provenance
Family 151: A <i>C</i><sup>1</sup> counterexample to the entropy conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Model researchers can flag the false implication from second-homology growth to orbit complexity for general C1 noninvertible maps.
Applicability and commercial boundary
The compact smooth counterexample does not invalidate more regular or invertible subclasses and does not create an entropy estimator.
Initial business decision
Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.
Next verification action
Extract a finite explicit description and the exact class excluded by the counterexample.
Evidence scope
The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.