An EAS-Supported Finite Electrodynamics Spectral Representation

This paper is archived as a speculative research work. We construct an EAS-supported finite representation of the known noncommutative-geometric electrodynamics factor. The finite input consists of two binary bounded-support labels: handedness H∈H_+,H_- and a second configuration label ∈+1,-1 associated with the Phase-0 path-facing boundary sense. Under the presently established EAS constraints no known rule excludes any of the four formal pairs, so their Cartesian product is adopted as the working finite representation domain X_F Z_2 Z_2; constructive realizability of all four pairs is not proved here. The finite assumptions themselves possess an H≤ftrightarrow exchange symmetry: exchanging which binary coordinate is resolved by the algebra and which is represented by the grading produces an isomorphic class of finite constructions. Accordingly, the present electrodynamics construction makes an explicit selection premise: H is the algebra-resolved coordinate and is the grading coordinate. On the minimal one-line-per-configuration carrier H_F^ := C^4, the selected algebra is A_F C^2, is represented by the balanced grading _F, and simultaneous reversal (H, ) (-H,- ) is represented by an antiunitary real structure J_F. Imposing self-adjointness, oddness, reality, and the first-order condition classifies the minimal-carrier 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). Conditional on the handedness-resolving electrodynamics selection, its two normalized weights are the two opposite electric-charge representation signs. 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 by the primitive labels and may carry additional finite multiplicity and a matrix-valued mass slot. Thus neither handedness as the physical charge selector nor minimal finite multiplicity is claimed as an EAS theorem. Numerical mass and coupling values, spacetime gauge fields, dynamical actions, and quantization remain downstream questions.