Abstract
The companion kinematic analysis reconstructs, conditionally, an oriented conformal-Lorentzian two-form carrier and Hodge operator but stops before an exterior derivative, potential, gauge group, source, charge, or action is supplied. This paper asks which additional structures are required to reach classical Maxwell theory and how far those structures can be embedded in the wider Complementarity-First/TCG/CUD program. First, any pointwise algebraic relation preserved by nonzero scalar rescaling is shown unable to imply dF = 0, and no nonzero GL(V)-natural fiber map V* -> Λ^2 V* can replace a differential. Under an explicit package of soldering, de Rham, one-form-potential, locality, quadraticity, constant-background, and variational assumptions, the most general real local quadratic first-derivative action is Maxwell kinetic plus a constant theta term, modulo boundaries. Hodge operation, electric-magnetic duality, and electromagnetic gauge redundancy are then separated: duality changes nonzero F, whereas gauge transformations leave F fixed, and a local duality angle introduces new derivative terms. Given a principal bundle, a connection is exactly a horizontal/vertical complement and curvature is its nonintegrability, but the space of connections is affine and no preferred splitting follows from complementarity alone. Compact U(1) further requires periodic transition data, integral curvature periods, and flat holonomy beyond the local law A -> A + dλ or the curvature F. Once an integral dyonic lattice is independently supplied, the Dirac-Schwinger-Zwanziger form gives a genuine symplectic cross-pairing, yet it selects neither the lattice, an electric polarization, a charge unit, monopoles, nor the observed source spectrum. Finally, an additional unitary central phase in a GL(2,C) link, together with a supplied periodic four-dimensional cochain complex, constitutive matrix, and Maxwell branch, yields an exact finite Abelian descendant with gauge invariance, Bianchi closure, current conservation, a BF-type algebraic first-order parent under a supplied pairing, flat holonomies, and six topological two-form sectors. Alternative constitutive, higher-derivative, normalization, and global choices certify nonuniqueness. The construction does not derive d, the potential formulation, compactness, charge normalization, monopole particles, continuum convergence, photon quantization, matter, or QED.
Where it sits in the release
CEM-P2 takes the arena as given and reconstructs Maxwell theory on it, step by conditional step: differential closure, gauge geometry, global charge, and an exact Abelian descendant. The discipline is in the bookkeeping — each step records what had to be supplied.
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