Scattering Signatures of the Equilibrium‑Mode Electron A.7

Add‑On A.7 extends the equilibrium‑mode architecture into the scattering domain, showing that elastic, inelastic, resonant, polarized, and high‑energy scattering behavior arise directly from deformation and interference of the electron’s internal oscillatory mode. Building on the structural invariants established in A.1–A.6—global energy law, angular geometry, transition symmetry, multi‑electron interference, ionization stability, and multicenter coupling—this add‑on derives scattering amplitudes, angular redistribution, quadrupole‑activation thresholds, resonance‑width scaling, and high‑energy compression from the same geometric and stability constraints that govern spectroscopy, fine structure, ionization, and bonding. The two‑axis angular geometry and polarity‑inversion boundary identified in A.2 generate the characteristic dipole‑dominant two‑lobe pattern at low energy, while deformation beyond the dipole‑stability limit activates quadrupole channels and produces dipole–quadrupole interference. Resonance behavior emerges when momentum transfer drives the internal mode toward unstable configurations defined in A.5, with resonance widths scaling with the stability margin. At high momentum transfer, radial compression suppresses angular structure, yielding the observed pointlike limit without invoking a point‑particle ontology. A.7 provides a full mathematical framework, structural rules, quantitative predictions, and a falsifiability structure spanning angular redistribution, polarization dependence, resonance scaling, and high‑energy collapse. This add‑on completes the scattering‑signature layer of Version 1.0 and serves as the bridge to A.8, where the same deformation and stability rules are extended into plasma behavior and collective mode structure.