Regularity and persistence in non-Weinstein Liouville geometry via hyperbolic dynamics

The paper’s Theorem 7.6/1.12 is internally consistent and supported by explicit lemmas (notably Lemmas 7.1–7.5) proving: (a) the Axiom A structure with Λ_T a finite union of periodic orbits and a hyperbolic plug whose core is Λ_L; and (b) under TΛ ⋔ ker α, Y|_Λ is synchronized Anosov and (W,α) is C^1–strictly Liouville equivalent to an LIS. The candidate solution reaches the same conclusions but contains two substantive flaws: (i) it asserts without justification that α_± := ι_{±n}dα|_{TΛ} are positive/negative contact forms with ker α_+ ⋔ ker α_-; the paper instead constructs α_u and α_s with α_± := α_u ∓ α_s to ensure contactness and transversality, avoiding the unsupported ι_{±n}dα claim; and (ii) it overstates uniform hyperbolicity on all of Λ \ Λ_T, whereas the paper carefully removes a neighborhood of Λ_T to obtain a hyperbolic plug with a hyperbolic core. There is also a local misstatement that dα(Y,·)=α(·)=0 on TΛ (false under TΛ ⋔ ker α). These errors affect the correctness of the model’s proof as written, though the final conclusions align with the paper.