Nuclear Magic Numbers as Rigidity Locks: Deriving the Periodic-Table Ladder with the D₄ Regulator

One may reasonably ask whether the canonical magic sequence is less a dynamical accident than a geometric inevitability; the present brick supplies an existence construction in that direction. We demonstrate, in the sense of an existence construction, that the standard nuclear-physics magic numbers 2; 8; 20; 28; 50; 82; 126 are realized as structurally rigid growth landmarks in the R4 lattice comprised of 24-cell building blocks. We present a neutral, regulator-first construction of the periodic-table ladder from closest packing in four dimensions, treating nuclei as aggregates of identical, strain-free 24-cell \dice" grown one attachment at a time in the D4 (equivalently R4) adjacency stage. The growth is ltered into two distinct classes of structural thresholds: capacity closures (Skin), where a shell becomes geometrically enclosed, and rigidity locks (Bones), where the induced adjacency acquires a symmetry-aligned truss that suppresses remaining shear and twist modes. Within this framework the canonical magic list is recovered exactly as a strict subset of rigidity locks, while additional intermediate rigidity nodes appear as internal bracing steps that are retained as structural waypoints but are not labeled magic under a stated strict sieve. This brick is deliberately prior to force laws: it exports a neutral sca old and an auditable stability ladder to be used by subsequent work that reintroduces proton charge-strain as a selection operator acting on the neutral adjacency bookkeeping; no uniqueness claim about stage or sieve is required at this step.