From EAS Spectral Geometry to Electrodynamics: Riemannian Quantization and Lorentzian Interpretation

Abstract

This paper is archived as a speculative research work. Starting from separately obtained EAS binary relational data and the selected minimal electrodynamics factor constructed in Paper I, we build qualified Riemannian and Lorentzian spacetime electrodynamics representations while maintaining a strict ontology/interface boundary. The Paper-I factor is used here with the frozen intrinsic antecedents H= rank–3 cyclic orientation and = Phase–0 exterior-connectivity orientation, in its selected orientation-resolved finite representation and minimal-carrier convention H_F=H_F^ = C^4; consequently every statement below about the two normalized relative-U(1) weights ±1, one finite Dirac multiplicity, one finite mass modulus, and Tr_H_F( H^2)=4 is a selected minimal-factor result, not an EAS theorem excluding the nonminimal carriers H_F^(k)= C^4 C^k. The September-1 bounded-support theorem stack supplies the upstream SF antecedent of massive-rest capability and, for the established electron-like motif, the exhaustive route class R_ AR=ABA,BAB/ reflection whose antireturn parity admits the standard spin- 12 interface representation and massive Dirac embedding . These physical-spin and Dirac carriers remain distinct from the finite NCG carrier. Independently, the charge theorem establishes, on the charge-eligible coherent handed bounded-support domain B_Q, the native signed class Q_b(B)=H_B=±1 . Paper I represents that class on the selected finite carrier by H|H, =Q_b(B)|H, , independent of . The separately established ordered-history operator Q_ or=P_+-P_- remains an auxiliary orientation representation and is not a charge prerequisite. The auxiliary Riemannian branch admits a Spin spectral host and its almost-commutative product with this finite factor. A relational-difference result identifies a direct antecedent for the spacetime spectral differential: a defined binary SF relationship supplies a relational scalar difference and collections of such differences define a finite relational differential d_A obeying the Leibniz rule. On an edge-separated irreflexive report scope the generated module ^1_ rel spans all represented directed-edge one-cochains and can carry arbitrary discrete u(1) connection coefficients. Three independent rank–3 differences determine only the spatial covector on their represented three-dimensional tangent span; a general fourth cotangent component requires an additional independently qualified datum. SOO overlap order-sensitivity and the NCG differential commutator are not identified as the same mathematical object, but both show that higher-scope representation cannot in general treat relational action and scalar state as independently pointwise/global. For the product algebra C^∈fty(M_E) C^2, the real-structure-trivial diagonal subgroup can be quotiented pointwise, giving the exact local group C^∈fty(M_E,U(1)). The Paper-I matter carrier and qualified photon/gauge carrier factor through this same relative quotient while remaining different spectral triples. Within the matter factor the product inner fluctuation leaves one represented relative direction, B_ =Y_ H, and the vanishing finite differential calculus produces no finite Higgs-type scalar. Thus the same local relative U(1) that supplies the vector-connection symmetry acts on charge-eligible bounded matter with normalized representation weight q:=Q_b(B)=H_B=±1. The one represented gauge direction is not a count of physical photon modes: on a separately qualified downstream free-Maxwell interface, a nonzero null momentum k has physical polarization quotient P_k=k^ /span_ Ck with _ C P_k=2. On the bounded-support Lorentzian interface, three independent exterior relationship images determine a positive spatial three-plane whose unique future unit normal u_B^ supplies a conditional provenance for the matter-current direction; no single exterior association is promoted to that role. After canonical normalization the Riemannian branch reaches the conventional Euclidean QED action and its standard functional-integral quantization entry. Independently, the reconstructed three-dimensional spatial geometry and the F1/F2/F3 report theorem establish a selected-direction Lorentz compatibility host. A global Lorentzian manifold, time orientation, global hyperbolicity, Spin structure, and Dirac–Krein analytic domain enter through an explicit F3-compatible global-completion gate. On such a qualified completion the Spin/Krein branch has invariant selected q=±1 sectors and reaches classical one-field Maxwell–Dirac electrodynamics. Complex Hilbert amplitudes, the Born rule, canonical quantization, renormalization, scattering theory, numerical e and m, a theorem uniquely forcing minimal finite multiplicity, and a complete electron/positron formation-conjugation classification are not derived here. The electron-like spin- 12 interface admissibility and the signed bounded-matter charge class are not open items in this paper.