Topological State Space Inference for Dynamical Systems

The paper defines slack distance (Definition 3.1) and proves Lemma 3.2: composing two certificates (s, ε) and (s′, ε′) yields a certificate for the endpoints with parameters at most (s+s′, ε+ε′). Its proof is concise, using a union-of-bad-indices argument, and then states as a corollary that any convex, 1-homogeneous aggregator d_π yields a triangle inequality and a Vietoris–Rips bifiltration in (t, r) (monotonicity) . The candidate solution provides a more explicit index-intersection construction and a trimming step to achieve exactly s+s′ in the nondegenerate regime, plus a detailed subadditivity argument for d_π and a clear monotonicity proof for the bifiltration. The two arguments agree in substance; the model’s proof supplies missing details and edge-case handling that the paper sketches but does not fully spell out. Overall, both are correct, with different levels of rigor.