Arbitrary-Coupling Ultraviolet Regulator Universality For a One-Dimensional Moving-Mirror Hamiltonian

We study a relativistic particle on a periodic ring whose internal harmonic oscillatorcouples through its momentum to a massless bosonic field. Each ultraviolet-regulatedHamiltonian contains a positive completed square and a logarithmically divergent vac-uum contraction. After subtracting the exact regulator-specific contraction, we con-struct a common, semibounded, self-adjoint limiting Hamiltonian for every fixed realcoupling. The construction uses a low-frequency completed-square reference and a smallhigh-frequency quadratic-form tail. We prove norm-resolvent convergence for uniformlybounded, modewise-consistent hard or soft regulators, without assuming small coupling ortruncating boson occupation numbers. A uniform two-stage resolvent estimate is of orderOg,B ( log K/√K) in the low-frequency threshold K. At coupling g = 1, exact rationalinequalities certify a shifted-resolvent comparison error below 3/1000 at K = 20000. Thelimiting form domain equals the free form domain. Its operator domain, however, excludesthe bare field vacuum for nonzero coupling. We also exhibit finite regulator-dependentenergy offsets that would survive an unmatched subtraction. None of these results assertsa positive ultraviolet spectral gap or constructs a nonperiodic infinite-volume model.