Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold

The paper states the rectified dark Poisson bracket (Eq. (3.61)) and the post‑Darwin Hamiltonian (Eq. (3.66)), and then gives the variational derivatives δH⋆PD/δfσ and δH⋆PD/δEL (Eqs. (3.68)–(3.69)), which, when inserted into the bracket, yield the closed evolution system (Eqs. (3.70)–(3.72)). The candidate solution reproduces these same ingredients: it computes the variations of H⋆PD (invoking the same self‑adjointness and Helmholtz–Hodge properties used in the paper), shows the same cancellations, and inserts the derivatives into the very same bracket to obtain the same equations and closure on (fσ, EL). It also correctly explains that Jacobi is secured by using the exact rectified bracket (paper’s symplectic rectification argument). In short, the model follows the paper’s method and matches the paper’s formulas and logic precisely .