Entropy equality and local symmetry in negative curvature

Comments and discussion

• Tristan Humbert, reaction in 100+ reactions to 100+ solutions, Proofs and Prompts (Proofs and Prompts, post dated 2026-10-08, reactions added through 2026-10-19). Humbert, author of a local version of the conjecture near real and complex hyperbolic metrics, calls the paper "mostly unreadable slop" and criticises OpenAI's publication standards and the verification burden placed on mathematicians, without presenting a specific mathematical refutation.

Related prior literature mentioned by others

• Tristan Humbert, Katok's entropy conjecture near real and complex hyperbolic metrics (arXiv:2409.11197, 17 September 2024; v3 2025-10-20). Humbert names this local version of the conjecture in his reaction above; it proves rigidity near real and complex hyperbolic metrics in dimension at least 3 and is cited in the paper as \citet{Humbert2026}.

Possibly relevant literature (found by the agent, not checked)

• Ursula Hamenstädt, Metric and topological entropies of geodesic flows (MPIM preprint MPI/90-17, 1990). Its Theorem A states that if the metric and topological entropies coincide, then horospheres have constant mean curvature; this partial result toward the same conjecture is not cited in the paper's "History and context" subsection.
• Ursula Hamenstädt, Entropy-rigidity of locally symmetric spaces of negative curvature (Ann. of Math. 131 (1990), 35–51). An earlier topological-entropy rigidity theorem for manifolds homotopy equivalent to a locally symmetric space, related to the minimal-entropy step in Proposition pre:smooth-rigidity, which the paper bases on Besson–Courtois–Gallot.
• Patrick Foulon and François Labourie, Sur les variétés compactes asymptotiquement harmoniques (Invent. Math. 109 (1992), 97–111, doi:10.1007/BF01232020; entry in Foulon's publication list). Concerns closed negatively curved asymptotically harmonic manifolds, the conclusion of Hamenstädt's Theorem A, and gives a related route from smooth invariant foliations to local symmetry alongside the Benoist–Foulon–Labourie step the paper uses.
• Yong Fang, Dynamical-geometric characterization of the geodesic flows of negatively curved locally symmetric spaces (Ergodic Theory Dynam. Systems 35 (2015), 2094–2113). Characterises rank-one locally symmetric geodesic flows among transversely symplectic Anosov flows with smooth weak distributions, related to the paper's final step from a globally smooth splitting to local symmetry (Theorem smooth:splitting and Proposition pre:smooth-rigidity).

Digests and expositions

• Latent Seminar, Entropy equality and local symmetry in negative curvature (7 October 2026). Outlines the manuscript's route from entropy equality through formal symmetry and transverse smoothness to local symmetry, treating the algebraic classification as an input and explicitly disclaiming independent verification of the complete proof.