Abstract
Within the Complementarity-First and Reciprocal Internal Complementarity research program, we study nonlinear perturbations of the supplied smooth massive monopole used in the two companion papers. The host is flat-space SU(2) Yang–Mills theory with one adjoint scalar, unit magnetic degree, and equal scalar and vector masses; neither its action nor its physical scales are selected by reciprocity. The exact cubic and quartic energy remainder is controlled in the covariant derivative-and-mass completion because every nonzero exterior gauge bracket contains a charged factor. A compatible nonlinear framed gauge and collective slice is constructed on the stronger class with square-integrable connection difference, and on its admissible exact gauge saturation. A logarithmically winding neutral rotation shows why this result cannot be extended to the entire original framed energy ball without changing the boundary convention or domain. At the actual configuration a coercive weak parameter problem gives the full nonlinear Gauss projection. A nondecaying boundary lift identifies a finite-norm charge direction, and an explicit rank-one correction produces the nearest constrained momentum of any prescribed finite real electric charge. Raw flux on unconstrained seeds is not a continuous kinetic datum and need not survive the ordinary projection. On an explicitly stronger compatible H3 graph-state class, a background-subtracted semilinear construction supplies local temporal evolution. The geometric constraints and Gauss law propagate; an integrable boundary-marker current gives conserved charge and a uniform framed flux limit. A time-integrated velocity estimate keeps the nonlinear chart available for a positive interval, producing an actual differentiable gauge and collective path with the mixed temporal equation. The inherited static energy bound then holds along that interval. The result is conditional local dynamics with declared charge and framing, not global nonlinear orbital stability, a stationary dyon, or a prediction of monopole abundance.
Where it sits in the release
The third paper of the magnetic trilogy. It establishes conditional local dynamics with declared charge and framing — not global nonlinear orbital stability, a stationary dyon, or a prediction of monopole abundance.
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