Abstract
Within the Complementarity-First and Reciprocal Internal Complementarity research program, we study the linear perturbations of the smooth massive magnetic core constructed in the companion paper. The host is a supplied flat-space SU(2) Yang–Mills theory with one adjoint scalar, unit magnetic degree, and equal scalar and vector masses. The action and physical scales are not derived from reciprocity. Starting from the full Cartesian second variation and linear Gauss constraint, we organize the physical angular sectors without excluding translations, boundary phase, or neutral radiation. A positive whole-half-line comparison gives a 4/25 lower bound in the two-profile magnetic radial sector. The separate spherical electric-flux operator has a positive but unquantified gap after charge and boundary data are separated. Explicit first-nonradial matrices, a compact-annulus Schur reduction, symbolic-angular-momentum higher matrices, and rational core certificates give all-angular nonnegativity conditional on the stated background and sufficient certificate predicates. The framed kernel consists of three translations and one phase tangent. In a covariant derivative-and-mass completion, a compact-remainder argument gives coercivity modulo this collective space with an unquantified positive constant. The kinetic wave operator nevertheless has essential spectrum [0,∞): exactly Gauss-dressed photon packets retain the zero threshold. An exact translation–photon overlap constructs fields orthogonal to the full kernel in L2 whose energy tends to zero while their local core tends to a nonzero translation. Thus energy-space or local-moment projection, not ordinary L2 orthogonality, is required for the stated coercivity. The result is a conditional linear sign, kernel, and norm-control theorem, not nonlinear orbital stability, decay, a numerical mode spectrum, or a monopole population prediction.
Where it sits in the release
The second paper of the magnetic trilogy. It is a conditional linear sign, kernel, and norm-control theorem — not nonlinear orbital stability, decay, a numerical mode spectrum, or a monopole population prediction.
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