Defect Migration in the D4 Vacuum Lattice: Hop Parity, Site Symmetry, and Soliton Kinematics

This paper studies how a localized defect migrates through the D4 root lattice. Its spatial slice is the face-centered cubic lattice, and the tetrahedral voids of that slice form a simple cubic sublattice, two-colored by coordinate sum modulo four. Four results follow. First, the exclusion geometry of a void closes its four face channels and leaves six edge channels open, so the coordination number six is derived and not assumed. Second, each void class admits exactly one bond-direction set, so a void carries one bit of orientation information. The matter/antimatter grading therefore cannot be the void class, and the worldline must carry it instead. This corrects an earlier identification of inversion-related voids with matter and antimatter: those classes are propagation sublattices. Third, the rotational site symmetry is T≅A4, whose double cover has faithful irreducible representations only in dimension two. Among the half-integer spins, j=12 alone stays irreducible on restriction. This selects a spin; it does not determine one. Fourth, a hop induces a canonical bijection on the bounding atoms by a lattice translation, and baryon species is preserved if the winding labels follow that bijection. One dynamical postulate is used. Under it a hop carries exactly one time step, no update leaves a defect in place, and a defect at rest oscillates between two adjacent voids. A closing section records the conditions under which a localized continuum solution obeys E=γErest; no such relation is derived here for the lattice defect, and that section is conditional throughout. Every geometric claim is verified by an accompanying script.