In this work, we develop a self-contained effective framework in which a gauge-invariant entanglement entropy functional serves as the microscopic motivation for a renormalizable portal connecting three structural elements: A non-perturbative modular gap defined operationally through reflection-positive lattice swap–swap correlators; A dimensionally consistent entanglement–Yukawa portal coupling to Standard-Model fermions; An Abelian information–gauge sector with a compact Stückelberg completion. The central objective is conceptual and structural: to demonstrate that a lattice-defined entanglement observable can be consistently uplifted into a local effective field theory without violating gauge invariance, dimensional analysis, or reflection positivity. A key result is that two observables—(i) the modular gap scale extracted non-perturbatively and(ii) the universal part of charged-lepton flavour-ratio scaling—are governed by the same effective parameters . This establishes a concrete lattice–continuum cross-check framework. The manuscript emphasizes internal consistency, EFT power counting, and falsifiability conditions rather than numerical claims. All phenomenological illustrations are explicitly labeled as pilot-level or conditional, and a full lattice reproducibility checklist is provided.
Ju Hyung Lee (Fri,) studied this question.