A CLASSIFICATION OF PSEUDO-ANOSOV HOMEOMORPHISMS VIA GEOMETRIC MARKOV PARTITIONS.

The paper proves the equivalence rigorously (Theorem 6) by building a universal symbolic model Σ_T via an equivalence relation ∼_T that depends only on the geometric type, showing Σ_T is a surface and the induced shift is conjugate to both maps; it also treats orientation carefully (Lemma 26/Corollary 7) and handles non-binary incidence via refinement . The candidate solution gives a plausible sketch but makes a critical mistake: it asserts a bijection π_f: Σ_T → S_f, whereas π_f is generally not injective on boundary points; injectivity only holds on the set avoiding partition boundaries. It also invokes a uniform continuity argument for extending the conjugacy from the dense set X_f that is not justified (continuity of the coding map s(·) is not established), and the orientation-preserving claim is only gestured at, not proved. Hence the model’s proof is incomplete/incorrect at key steps, while the paper’s argument is complete.