CSP-03: Shell Atomization, Spectral-Variance Geometry, Approximate Eigen-Shells, and Resonant Transfer

Shell Atomization, Spectral-Variance Geometry, Approximate Eigen-Shells, and Resonant Transfer

CSP-01 reduces same-instant mid-strain/frequency-window synchronization failure to D_win∨D_shell∨D_space; CSP-02 splits the spatial branch into singular-core alignment, local window mismatch, local shell atomization, and super-parabolic micro-packing. This round attacks D_shell (partially attacking D_(I,sh)). The core question: if the relevant strain state avoids a single dyadic carrier by dispersing across many shells, must the exact approximate-Laplacian-eigenfunction residual necessarily grow? The answer: yes, under severe global shell atomization. Proves projection monotonicity of the approximate-eigenfunction residual, a two-cluster spectral-separation lower bound, a universal residual-gap theorem under severe sharp dyadic shell atomization, and same-instant synchronization when the atomized spectral window captures a fixed fraction of the mid-strain UV spike. Distinguishes bounded window-edge leakage plus local-core/global-spectral alignment from genuine spectral dispersion, and gives a conditional resonant-transfer dispersion theorem.