Effective Vertex and EFT Encoding of Electron Structure in QED

This work develops a controlled effective-field-theory (EFT) formulation for encoding admissible internal electron structure into the established framework of quantum electrodynamics (QED). Building on earlier studies that introduced and characterised admissible finite-energy electron core configurations and their spectral and phenomenological properties, the present analysis completes the representational chain by translating real-space structural information into momentum-space form factors, effective QED vertices, and higher-dimensional operator structures. The framework preserves gauge invariance and infrared universality while making explicit the hierarchy of scale suppressions that governs the experimental visibility of internal structure. It establishes a transparent and model-independent mapping between admissible real-space configurations and experimentally constrained observables, including form factors, compositeness bounds, and effective interaction scales. The analysis demonstrates that admissible internal structure can be consistently encoded within the existing field-theoretic structure of QED without introducing new degrees of freedom or modifying the underlying gauge symmetry. Structural effects remain intrinsically suppressed in infrared-dominated regimes and become experimentally relevant only at sufficiently high momentum transfer, where effective-field-theory suppression is reduced. By completing the effective quantum-electrodynamic encoding of admissible finite-energy core configurations, this work provides a systematic interface between structural hypotheses and phenomenological constraints, and establishes the QED/EFT representation layer of the finite-energy electron core research programme.