Quantitative contact Hamiltonian dynamics

The paper defines c(h,θ) via the persistence module P(W,h) = {HF∗(η#h)}η indexed by R\Sh and proves properties (1)–(6) in Theorem 2.11 using zig–zag isomorphisms, a new pair-of-pants product on contact Hamiltonian Floer homology (Theorem 2.12), and technical lemmas (e.g., Lemma 6.1 for spectrality, Proposition 6.2 for descent) . The candidate solution reproduces the same invariant and the same list of properties with a largely standard Floer-theoretic outline (continuation, monotonicity, time-shift, product, and stability), but it assumes the contact-level pair-of-pants product and spectrality mechanisms rather than deriving them in the new gapped-module framework; the triangle inequality and stability bounds match the paper’s statements (including the 2·max{oscR h, oscR g} term) . Hence, both are correct; the paper’s proof is novel in its analytic construction and algebraic packaging, while the model sketches a parallel, classical-style argument.