What was already known
Shub’s general C¹ self-map conjecture predicted entropy at least the logarithm of the homological spectral radius. Earlier Lipschitz counterexamples did not settle the C¹ question, and positive results covered restricted map classes.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Disproves the general C¹ self-map formulation of Shub’s entropy conjecture.
Limitations
The constructed map is noninvertible; the selected claim does not refute a version restricted to diffeomorphisms.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned OpenAI Lean scope note identifies this selected claim.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- A noninvertible C¹ self-map of a compact smooth manifold without boundary has zero topological entropy while its induced action on second real homology has eigenvalue 2.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision