Structurally stable non-degenerate singularities of integrable systems

The paper proves strong topological structural stability for compact non-degenerate semilocal singularities satisfying the connectedness condition via a Vey-type normal form, a Principle Lemma that propagates the Vey momentum map across the fiber, and Zung’s topological classification; it concludes with a left–right equivalence after normalizing by target diffeomorphisms. The candidate solution reaches the same theorem but inserts an analytic factorization step (Stein factorization on complexifications) to recover a base diffeomorphism. This additional step is not used in the paper but is plausible in the analytic category. Aside from minor extra assumptions (properness/connected fibers for the holomorphic factorization) and not explicitly invoking the non-splitting condition in the classification step, the candidate’s argument aligns with the paper’s structure. Hence both are correct, with different proof styles.