A Finite Electrodynamics Factor for an SF-Supported Lorentzian Noncommutative-Geometric Interface

This paper is archived as a speculative research work. We adopt, re-express, and verify the known finite electrodynamics factor used in an almost-commutative description of charged Dirac matter, placing it in the conventions of an SF-supported Lorentzian noncommutative-geometric interface. The finite algebra $A_F=\mathbb{C}^2$ acts faithfully on $H_F=\mathbb{C}^4$ by $\pi_F(a,b)=\operatorname{diag}(a,a,b,b)$. In the frozen basis we specify the finite fundamental symmetry, grading, normalized charge operator, bounded real Dirac-parameter family, and finite real structure $J_F=C_F$, and verify their adjoint, grading, reality, order-zero, and first-order relations. The reality signs are those of conventional finite KO-dimension six. The canonical total-even product contains one independently specifiable Dirac-spinor slot in each opposite-charge sector, with no additional finite flavor or generation multiplicity. The finite real structure establishes antiunitary equivalence of the finite charge representations but does not impose product-level field dependence. The finite unitary representation has a diagonal kernel and one represented relative $U(1)$ direction, while the finite one-form and scalar sectors vanish. Conventional zero-dimensional orientability is not satisfied by the displayed representation, and no complete total Lorentzian real spectral triple or fermionic action is claimed. The construction is therefore a verified selection of prior finite electrodynamics data compatible with, but not derived from, the admitted SF charge characters and spatial geometry.