This work develops the dynamical spectral and momentum-space characterisation of the finite-energy electron core framework established previously (doi:10.5281/zenodo.18668813). Within this controlled real-space formulation, admissible smooth finite-energy core configurations are analysed using the associated radial Sturm–Liouville operator, yielding a discrete internal eigenvalue spectrum with a large confinement-induced excitation gap. The analysis establishes a precise ultraviolet–infrared correspondence: infrared observables depend only on the root-mean-square radius and remain universal across admissible configurations, while ultraviolet behaviour is governed by the detailed spatial structure of the core and produces controlled momentum-dependent deviations from the point-like limit. The resulting electromagnetic form factor remains indistinguishable from unity throughout experimentally accessible infrared regimes and deviates significantly only at momentum scales determined by the confinement radius. These results demonstrate how smooth finite-energy real-space confinement provides a mathematically well-defined ultraviolet-finite description that remains fully consistent with established phenomenology. The present work constitutes the dynamical spectral continuation of the finite-energy core framework and establishes a structural and phenomenological baseline for future investigations of compositeness constraints, spectral stability, and momentum-space signatures of admissible real-space configurations. This Zenodo record provides the full manuscript and serves as part of a structured research programme investigating finite-energy electron core models and their phenomenological consequences.
Doğan Yılmaz (Wed,) studied this question.