Anisotropic Orientational Transport Geometry in a Finite-Energy Electron Core

This work investigates whether the low-lying collective deformation sector of a previously constructed finite-energy electron core develops a coherent orientational transport geometry under finite rotational transport. The analysis combines rotational-overlap diagnostics, infinitesimal generator extraction, rotational leakage measurements, symmetry-adapted mode-family decomposition, principal-component analysis of rotational responses, finite rotation-loop transport, BCH-normalized curvature tensors, randomized null controls, basis-truncation tests, and grid-robustness studies. The results show that the orientational structure is not isotropic and does not form a closed rigid rotational multiplet. Instead, finite rotations generate organized off-diagonal mixing, leakage into higher deformation sectors, stable finite-loop drift, and robust low-dimensional transport organization. More than 99.5% of the rotational-response variance is captured by the first three PCA transport directions, while randomized null controls fail to reproduce the observed collapse. The curvature structure is dominated by symmetric deformation transport rather than closed infinitesimal Lie-algebraic rotation. Independent transport, curvature, PCA, eigenspectrum, localization, and scattering diagnostics repeatedly converge toward the same anisotropic transverse-paired transport hierarchy. The same axial organization previously identified in directional momentum-space form factors reappears consistently in the orientational transport geometry. The resulting picture is therefore not that of a rigid spinning sphere, an exact SU(2) multiplet, a spin-1/2 derivation, or a contradiction with QED. Instead, orientation emerges as organized nonlinear finite-deformation transport within the collective sector of a localized finite-energy electron core. This work extends the finite-energy electron-core research program by connecting spectral organization, deformation-shell structure, and momentum-space phenomenology with an emergent orientational transport geometry.