On a classification of axiom A diffeomorphisms with codimension one basic sets and isolated saddles

The candidate solution reproduces the paper’s invariants and equivalences for S_k, P_k, and M_k almost verbatim: (i) S_k: equivalence of k-tubes under linear automorphisms whose determinants share a common sign, together with a1+b1=a2+b2 and c1=c2, and the manifold decomposition M^n ≅ #^k T^n, with k+a+b=c+2 and admissibility of t(f) (Theorem 1 and Lemma 2.1) ; (ii) P_k (n∈{8,16}): classification by graph Γ_P with a marked edge carrying a Pontryagin number from the stated Eells–Kuiper range, and the requirement that the linear conjugacies have positive determinant; commensurability of graphs ⇔ global conjugacy (Theorem 2 and its construction) ; (iii) M_k: classification by Γ_M with three marked vertices and two adjacent marked edges; determinants must have a common sign (Theorem 3 and construction notes) . The orientation/sign mechanism used by the model (orientation on characteristic spheres encodes the sign, and extension across annuli requires consistent orientation) matches Lemma 1.2 and Proposition 2 in the paper . The candidate’s description of the complement as annuli plus a single “polar block” coincides with Lemma 1.4 (for P_k and M_k) . One minor overstatement is the claim that, in S_k, the incidence pattern forms a chain; the paper does not explicitly assert a “chain” property (it obtains admissibility and k+a+b=c+2 by other means), so that part could use a citation or a short proof. Otherwise, the reasoning and outcomes align closely with the paper.