An EAS-Supported Finite Electrodynamics Spectral Representation

Abstract

This paper is archived as a speculative research work. We construct an EAS-supported finite representation of the known noncommutative-geometric electrodynamics factor and update its provenance using the established bounded-support and charge theorem stacks. The common finite carrier is a higher-scope representation of relational distinctions, not a primitive SF state. The finite input contains the bounded-support cyclic rank–3 handedness H∈H_+,H_- and the distinct Phase–0 exterior-connectivity orientation ∈+1,-1. Their Cartesian product is retained as the working finite representation domain X_F Z_2 Z_2; constructive realization of all four formal pairs is not claimed. The revised bounded-support stack establishes persistent nonfree recurrence as the SF antecedent of massive-rest capability and, for the established nine-point electron-like motif, uniquely selects the antireturn recurrence class R_ AR=ABA,BAB/ reflection with Φ -Φ Φ. That native parity admits the standard spin- 12 interface representation and massive Dirac embedding; these spin and Dirac carriers remain distinct from the finite NCG carrier used here. The charge theorem independently establishes, for a charge-eligible coherent handed bounded support, the completed charge report _H=H(1,1,1) and the normalized signed matter class Q_b=H=±1. This class is the SF antecedent represented by the electromagnetic U(1) matter weight; no additional ontological charge object is required. On the selected minimal carrier H_F^ := C^4, the finite algebra is A_F C^2, is represented by the balanced grading _F, and the antiunitary real structure J_F implements the selected finite conjugation. Self-adjointness, oddness, reality, and first order classify the finite Dirac operator up to compatible unitary equivalence by one nonnegative modulus m_F. The combined direct and opposite unitary actions have diagonal kernel, leaving one faithful relative group U(1)_ rel generated by H=diag(1,1,-1,-1). Its eigenvalue on |H, is H=Q_b and is independent of . The companion spacetime construction identifies this same quotient with the local electromagnetic U(1) connection architecture, so the charge-provenance chain is now charge-eligible handed bounded support → Q_b=H=±1 → H → U(1)_ EM matter representation. The separately established ordered-history operator Q_ or=P_+-P_- remains a valid auxiliary orientation representation but is no longer a prerequisite for electric-charge assignment. The classified minimal-carrier Dirac operator commutes with the represented algebra, so ^1_D_F(A_F)=0 and no finite Higgs-type scalar inner fluctuation is generated. Nonminimal carriers H_F^(k)= C^4 C^k are not excluded. Numerical mass and coupling values, complete particle/conjugation classification, spacetime gauge-field configurations, dynamical actions, and quantization remain downstream questions.