Electromagnetism on the cubic sublattice of the FCC vacuum: the correct photon polarization count, and masslessness from centrosymmetry

A vacuum modeled as a face-centered-cubic lattice carrying a quantum error-correcting code, with one qubit per nearest-neighbor bond, must find room for a gapless photon alongside the code and the gravitational strain sector. The nearest-neighbor <110> network cannot supply one. Its one-form sector has only one propagating polarization per site, and it is non-bipartite, so a compact U(1) theory on it is gapped. A simpler structure in the same packing does the job. The FCC nodes and the octahedral voids together form a simple cubic lattice, and a one-form gauge field on its <100> links has exactly one pure-gauge and two transverse modes per site: the Maxwell count, and a property of the complex needing no dynamical assumption. The sublattice is bipartite, so a Coulomb phase exists; its links are disjoint from the code's qubits, so the two algebras commute trivially; and its bond star is centrosymmetric, so no piezoelectric coupling exists at all, which protects masslessness without a gauge-invariance argument. Matter couples to the sector without any added interaction, since a <110> hop is the composition of two <100> hops through a void, and the ambiguity between the two covering paths is the flux through a cubic plaquette. Only this sector moves: non-bipartiteness is fatal for the photon, neutral for the weak sector, and an asset for color confinement and fermion doubling. Putting qubits rather than a gauge field on the same links gives the three-dimensional toric code, so the packing carries two CSS codes on identical qubit counts at opposite ends of the rate-distance trade-off. The construction also admits alpha = 1/137, which the pyrochlore route does not, though the coupling remains a free parameter.