A Canonical 2T + 1O Spatial Carrier for Coupled Gauge, Fermionic and Metric Kinematics

We examine a spatial carrier whose constituent cell consists of two whole tetrahedra at-tached to opposite triangular faces of one whole octahedron. In the regular face-centred-cubicgeometry the union is a rhombohedral fundamental domain and translates without voids orinterior overlap. This geometrical statement does not specify the dynamics. We thereforeseparate assigned fields and actions from results obtained on the canonical carrier. A compactU(1) electric kernel and covariant fermion Hamiltonian admit a positive finite-volume trans-fer and an all-site residual Gauss projection under explicit conditions. Finite-volume testsseparately support local electroweak/Yukawa routing, an SU(3) Wilson transfer, and metricresponse. Our new simultaneous open-patch witness places U(1) × SU(2) × SU(3) transport,Higgs/Yukawa blocks and a common metric shear in one non-factorised 24 × 24 one-body op-erator. Its sampled 96 × 96 transfer is positive (minimum eigenvalue 0.03807) and covariantto 4.71 × 10−16 relative error. These are existence and compatibility results for a chosen finiteaction, not a derivation of the Standard Model, a physical photon, Einstein gravity, a graviton,or a continuum quantum field theory. We give explicit failure criteria and distinguish thiscarrier from other dual or body-centred decompositions.