A Relational Antecedent of the QED Photon: SBB Structure, Local U(1), Lorentz Compatibility, and the Physical Polarization Sector

This paper is archived as a speculative research work. We develop a theorem-controlled correspondence between the Scalar Fields (SF) formalism of Entanglement-Algebraic Spacetime and the free-photon sector of quantum electrodynamics. The construction begins without a photon object in the SF ontology. Its primitive relational input is the symmetric binary relationship, or SBB occurrence. Scope-qualified SBB relationships generate a relational differential d_A and a first-order module ^1_ rel . Under a qualified spectral representation and a two-point finite geometry with D_F=0 , this structure provides a pre-interface antecedent of the represented local U(1) connection carrier. Independently, a narrowly defined free-SBB relational normalization supplies the premises used by the F3 construction to obtain a conditional selected-direction Lorentz host. The two branches meet only after adoption of a compatible flat free-field completion that preserves both established structures. Standard free Maxwell theory then yields the physical polarization quotient P_k^ QED = (k^ )/(span_ Ck), _ C P_k^ QED=2, and standard positive-frequency bosonic quantization yields the one-particle free-QED photon sector. A separate auxiliary result establishes polarization provenance. For a qualified rank-3 SBB organization, an independently admitted conjugate cyclic scalar relation and stated spatial-interface hypotheses imply a real two-dimensional transverse carrier T_r and a distinguished real projective ray [t]∈ P(T_r) . Under Common Spatial-Direction Compatibility and the independently established Maxwell/QED polarization quotient, the complexified carrier admits a qualified isomorphism T_r^ C \; \; P_k^ QED. This auxiliary correspondence does not derive the physical two-mode count, arbitrary polarization preparation, or helicity from SF structure. Throughout, strict dependency firewalls separate SF-native scalar variation, exchange, recurrence, and association structure from downstream gauge, spacetime, momentum, polarization, and quantum-field-theoretic quantities. The resulting claim is therefore a correspondence from SBB-derived relational structure to the free-QED photon sector, not an identification of an SF object with a photon.