Scalar Fields to QED: Closed Representation Translation and Reduced Native Representational Structure

This paper is archived as a speculative research work. Quantum electrodynamics represents charged spin-1/2 matter and electromagnetic interaction through a Lorentzian spacetime description containing Dirac spinors, a local U(1) connection, electromagnetic curvature, charge coupling, conserved currents, and formal quantum-field quantization. Entanglement–Algebraic Spacetime (EAS) uses a different mathematical organization: Scalar Fields (SFs) are described through scalar values, binary relations, rank-3 association structure, handedness, recurrence, relational accommodation, photon-like relational carriers, and bounded-support/compositional structure. This paper establishes a closed representation translation from certified SF antecedents into the standard kinematic, electromagnetic, Dirac, and U(1) structures entering minimally coupled QED, through the conventional QED action and standard formal quantization entry. The result is a representation correspondence, not a claim that QED mathematics is native SF structure. A second result concerns representational economy. Across the certified charge, photon/gauge, and kinematic sectors, multiple mathematically distinguishable interface roles trace to fewer type-distinct SF antecedent families. On the fixed certified comparison ledger, three SF antecedent families support eight unconditional interface roles, with a conditional extension to ten where the local kinematic limit and differentiability gates are satisfied. The significance of this count is not the raw number itself, but the repeated many-to-one provenance pattern across independently typed sectors. The SF formulation therefore exhibits lower native representational differentiation than its QED-supporting interface representation over the certified scope. This does not establish absolute mathematical minimality, an invariant global complexity measure, or computational superiority. Kinematics is central to the translation. In the SF formulation, displacement, average velocity, local velocity, and acceleration need not be introduced as separate native variables. They are represented from a discrete relational accommodation record through interval accommodation density and an independently defined interface-refinement map. For each admitted relational-path report, the resulting signed interface velocity readout obeys |v_P|≤q c, with local continuum quantities defined only when the corresponding universal refinement limits exist. No generic multidimensional velocity-norm bound is inferred from the one-path theorem alone. Thus even the kinematic variables on which the Lorentzian QED representation is formulated belong to the interface layer rather than to the native SF mathematical description.