Anti-classification results for conjugacy of diffeomorphisms on manifolds

The paper proves the target statement directly by a concrete Borel reduction [0,1]^ω/c0 ≤B topological conjugacy of C∞ diffeomorphisms on any manifold with dimension ≥ 2 (Theorem 5.1), yielding Theorem 1.1 that the conjugacy relation is not classifiable by countable structures; see the statement of Theorem 1.1 and the construction with auxiliary functions ψ and m, plus the turbulence/bireducibility facts used for [0,1]^ω/c0 . By contrast, the model’s argument hinges on a claimed Denjoy–Rees–type C∞, Borel-uniform realization T ↦ Φ(T) with canonical markers that reduces minimal Cantor-systems conjugacy to diffeomorphism conjugacy; this construction is neither presented nor justified in the paper and the cited 2025 preprint here does not supply that method (it uses the c0-coding construction instead). Hence the paper’s result is correct, while the model’s claimed proof path is unsupported by the paper.