Spectral Stability and Phenomenological Constraints of the Finite-Energy Electron Core

This work develops the phenomenological and stability analysis of admissible configurations within the finite-energy electron core framework established in previous studies (https://doi.org/10.5281/zenodo.18668813, https://doi.org/10.5281/zenodo.18686243). The finite-energy core model provides a mathematically regular alternative to the point-particle idealisation of the electron, eliminating classical self-energy divergences while remaining consistent with established infrared phenomenology. The present study establishes a quantitative correspondence between admissible real-space configurations and experimentally constrained momentum-space observables through analysis of the associated electromagnetic form factor. Infrared observables remain governed primarily by the root-mean-square radius, while ultraviolet behaviour depends on the detailed structure of the core profile, producing controlled and quantifiable deviations at high momentum transfer. Experimental constraints from precision QED measurements, atomic spectroscopy, and high-energy scattering define an admissible region in parameter space within which finite-energy core configurations remain phenomenologically viable. In addition, direct numerical evaluation of the second variation operator demonstrates spectral stability within the admissible class of perturbations. No negative eigenvalues are observed within numerical resolution apart from symmetry-related neutral modes, confirming that admissible configurations correspond to locally stable stationary solutions of the underlying energy functional. The analysis establishes the conditions under which extended finite-energy electron core configurations remain consistent with existing experimental constraints and identifies potential signatures accessible in future high-energy measurements. This Zenodo record provides the complete manuscript as part of an ongoing research programme investigating mathematically regular, finite-energy descriptions of electron structure and their phenomenological implications.