Structured Transition Rules and Anisotropic Spectral Gaps in ECSM Electron-Like Bound Shells

This paper reports the V14 stage of the ECSM electron-like packet programme. Building on the V12/V13 response-well bound shell hierarchy, the work tests whether ECSM electron-like bound shells can support structured transition rules, spectral gaps, anisotropic multiplet broadening, chi-deformed gap shifts, and determinant/exclusion stability within the same scaffold. The construction inherits four response-well bound shell levels with capacities 2, 6, 10, and 14, orbital degeneracy ladder 1, 3, 5, and 7, and cumulative closure sequence 2, 8, 18, and 32. The generated catalogue contains 32 finite bound modes. A dipole-like transition rule with Δl = +1, Δm = 0, ±1, and conserved internal state produces 54 allowed transitions organised into three neighbouring-shell families: l0 → l1, l1 → l2, and l2 → l3. In the isotropic limit, each transition family collapses to a single spectral gap. Under controlled anisotropy, the same allowed transition families broaden into multiplet-like gap distributions, with maximum width 0.08000000000000007 in the main run. A chi-deformation scan preserves the allowed transition count and transition family count while shifting the mean allowed gap by 0.11204734496828629. Background determinant tests confirm duplicate occupancy collapse, allowed same-group two-internal filling, valid closure filling, and forbidden duplicate overflow. The V14 notebook passes all 25 final criteria. The final verdict is: PASS: ECSM bound shells generate structured transition rules and anisotropic spectral gaps. This result is not claimed as a full derivation of atomic spectroscopy. It is a controlled transition-rule and spectral-gap bridge showing that ECSM bound shell modes can support selection-rule-like transitions, anisotropic multiplet splitting, chi-deformed gap shifts, and determinant/exclusion stability in one coherent electron-like packet scaffold.