Gutierrez-Sotomayor Flows on Singular Surfaces

The paper proves a global realizability theorem (its Theorem 10) under two alternative, vertex‑wise families of local constraints (Lemma 2 or Lemma 3), by choosing a canonical distinguished branched 1‑manifold for each weight and then gluing compatible isolating blocks; this is sound and explicitly stated to be sufficient (and far from necessary) . The model proposes an alternative construction: fix a canonical boundary model Γ_k for each weight and realize each vertex via 2D “pants + collars,” then glue exits to entries with identical Γ_k and smooth a global Lyapunov function. This recovers exactly the paper’s global gluing strategy in spirit (uniform boundary choices per weight), and it matches the same local constraint families: the model’s “Case A” aligns with Lemma 2 (Table 20 family) and “Case B” aligns with Lemma 3 (Table 19 family) . However, the model incorrectly states that its A/B lists are “exactly the necessary” local conditions; the paper shows they are sufficient and explicitly not necessary (see Example 7 and the remark after Theorem 10) . Aside from this overclaim and some unproved implementation details (e.g., guaranteeing GS dynamics while performing pants decompositions), the model’s main conclusion matches the paper’s sufficient condition theorem.