A Poincaré-Birkhoff Theorem for Asymptotically Unitary Hamiltonian Diffeomorphisms

The paper proves the result via filtered Floer homology, non-resonant homotopies, and a carefully constructed prime-iterate scheme that controls both action-shifts and grading-shifts. The candidate solution ignores the central ‘iterate obstruction’ in the unitary-at-infinity case and relies only on global Floer homology being Z/2 in one degree and a “degree-gap” heuristic. Without filtered homology and continuation between suitable iterates, the model’s cancellation argument does not preclude that all extra generators come from the finitely many original fixed points, so it does not actually force new primitive-period orbits. The paper’s proof directly addresses these difficulties; the model’s does not.