The Electromagnetic Sector of the Selection–Stitch Model: A Compact U(1) Field Beside a Stabilizer Code on the FCC Lattice

The Selection–Stitch Model (SSM) treats the vacuum as a face-centered-cubic (FCC) lattice whose ⟨110⟩ bonds carry a stabilizer code but no propagating electromagnetic field. We construct its electromagnetic sector by asking where a compact U(1) gauge field can live without sharing the code’s variables, comparing the Gaussian spectrum of the compact U(1) Hamiltonian on three candidate complexes. With triangular plaquettes, the ⟨110⟩ network supports a two-polarization photon, but only on the code’s bonds. On the code complex, whose two-cells are the octahedral checks, four zero-frequency flat bands appear, with harmonic dimension equal to the code’s logical count, 2L3+2. The ⟨100⟩ links joining FCC nodes to octahedral voids form a simple cubic lattice that shares no bond with the code and has the Maxwell count: this is the proposed sector. Gauge invariance keeps its photon massless even when the two site types differ, and centrosymmetry removes the leading strain coupling. Matter hopping along a ⟨110⟩ bond passes through an octahedral void, coupling minimally to the gauge links. In four dimensions, the cubic lattice is a slice of D4*, whose point group W(F4) makes the Euclidean photon isotropic through quartic order. With qubits instead of a gauge field, the same links form the three-dimensional toric code.