From Certified Nonlinear Contrast to Absolute Receiver Obstruction in Superconducting Models

Nonlinear slices, boundary data and finite-time propagation Part of Complementarity-First research and its Reciprocal Internal Complementarity (RIC) branch, this work studies nonlinear perturbations of the supplied smooth massive monopole used in MC-I and MC-II. The host is flat-space SU(2) Yang–Mills theory with one adjoint scalar, magnetic degree one, and equal scalar and vector masses. Its action and physical scales are supplied, not selected by reciprocity. The manuscript controls the exact cubic and quartic energy remainder in the covariant derivative-and-mass completion, using the charged factor in every nonzero exterior gauge bracket. It constructs a nonlinear framed gauge and collective slice on the stronger class with square-integrable connection difference, or an admitted exact prealignment into that class. A logarithmically winding neutral rotation demonstrates why the same strict slice statement cannot cover the entire original framed energy neighborhood. At the actual configuration, a weak parameter problem supplies the nonlinear Gauss projection. An affine boundary class defines the finite-norm charge direction, and an explicit correction gives the nearest constrained momentum of any prescribed finite real electric charge. An unconstrained seed's raw flux is not a continuous kinetic datum and need not survive ordinary projection. On an explicitly stronger compatible H3 graph-state class, a background-subtracted construction gives regular local temporal evolution. Geometric compatibility and Gauss propagate; integrable charge and energy currents yield conservation and a uniform framed flux limit. A separate velocity estimate supplies a positive interval inside the localized chart, with a differentiable gauge/collective path and the mixed temporal equation. The inherited static energy bound then applies along that interval. The supplement contains complete source inputs and the recorded finite-check replays, plus a companion Lean 4.19.0 project whose recorded local run checks 74 enumerated algebraic, arithmetic and conditional statements under explicit hypotheses. This is not full-paper formal verification: the nonlinear framed chart, physical charge construction, local field evolution and conservation/flux-limit proofs retain written analytical dependencies. Two internal AI source-bound reviews are not external specialist peer review. The work does not prove global nonlinear orbital stability, construct a stationary nonlinear dyon, select a physical mass scale or monopole abundance, or explain experimental non-detection. The lifespan and neighborhood constants are not numerically enclosed.