On solutions to the continuum version of the Kuramoto model with identical oscillators

The paper proves global C1 well-posedness for the continuum Kuramoto PDE with identical oscillators via an iterative (Picard-type) scheme and characteristics, derives the closed projected-characteristic ODE, and establishes global synchronization (C(t)→1) with at most one exceptional label; these are documented in their Theorem 1 (existence), Theorem 2 (uniqueness), the characterization (204)–(205), and Lemmas 10–14 for asymptotics . The candidate solution reaches the same conclusions but constructs the solution directly in label space by a globally Lipschitz ODE on the circle and then reconstructs ρ via the Jacobian; its asymptotic analysis parallels the paper’s (monotonic order parameter, invariant semicircle, at most one antipodal trajectory, and C(t)→1). The only substantive discrepancy is a minor typographical slip in the paper’s representation (204), where y(t;u) should read y(s;u) inside the time integral; the candidate correctly notes and fixes this. Overall, both proofs are correct and consistent, but methodologically distinct.