Operator-Derived Transition Amplitudes, Coherence-Gated Sum Rules, and Family-Leakage Diagnostics in ECSM Electron-Like Bound Shells

This work reports the V15c extension of the ECSM electron-like packet matter-sector sequence. Building on the prior V8c–V14 chain, the notebook replaces the V14 radial-overlap transition proxy with an explicit ECSM response-transition operator and computes operator-derived matrix elements, amplitudes, and strengths. The test inherits the fixed electron-like packet scaffold, Dirac-sector alpha/beta closure, response-centre bound shell energies, shell-capacity hierarchy, and determinant/exclusion background. In the coherent regime, V15c produces 54 allowed transitions across the three families l0->l1, l1->l2, and l2->l3, with forbidden transitions suppressed to zero numerical strength. Controlled anisotropy splits the transition gaps while preserving coherent family strength sums with zero measured drift. The notebook also identifies degraded-regime family leakage: excessive anisotropy or low chi introduces an additional reversed family, l3->l2. This is interpreted as a finite-response boundary diagnostic rather than a coherent-regime failure. The result is not claimed as a full derivation of physical oscillator strengths, atomic spectroscopy, QED, or the physical electron. It is a reproducible structural bridge showing that ECSM electron-like bound shells can support operator-derived transition amplitudes, coherence-gated response-strength sum rules, and degraded-response family-leakage diagnostics.