Complementarity Before Electromagnetism: Paired Kinematics, One-Time Geometry, and Conditional Four-Dimensional Hodge Structure

Can the kinematic arena of electromagnetism be reconstructed from a primitive complementary relation without assuming the electromagnetic field, Hodge duality, four-dimensional spacetime, or Maxwell's equations? This paper gives an assumption-controlled answer. A regular finite complementary pair reduces to the polarized carrier A ⊕ A*, which canonically carries a split metric, a symplectic form, and an involutive grading K^2 = I. Full polarized naturality, however, selects neither a sector exchange nor a real complex structure J^2 = -I; a constitutive polarity is additional data. Importing the one-time rank-two carrier of the companion Time analysis, the exterior square splits into complement-odd and complement-even sectors of dimensions m and binomial(m,2). An invertible complement-odd sector exchange therefore forces m = 3, conditionally on the selected two-form degree and the exchange map; no equation J^2 = -I is required for this dimension count. An alternative Klein-quadric incidence selector reconstructs the same four-carrier at paired rank three. After explicit reciprocity, closure, reality, and Lorentz-admissibility hypotheses are supplied, the standard constitutive correspondence yields a conformal Lorentzian Hodge structure; the paired carrier does not select that structure. The exact spinor identity Λ^2(S_+ ⊗ S_-) ≅ Sym^2 S_+ ⊕ Sym^2 S_- reconciles the paired-spinor and bivector routes, while complement parity exchanges Hodge chirality. The construction does not derive the two-form degree, a preferred metric or orientation, spacetime soldering, the exterior derivative, Maxwell dynamics, compact U(1), charge, or QED.