A Minimal 24-Cell Encoding of: YM Form for SU(3)×SU(2)×U(1), QCD Holonomy, and Three Families

We present a minimal, composable set of pre-@() properties on a single 24-cell regulator K that map under @() to the form of the Standard Model gauge sector. We define edge-holonomy variables for U(1), SU(2), and SU(3), and we define curvature and energy on triangular faceloops as a Wilson plaquette functional on the 24-cell 2-skeleton with defect support excised. We close the previously-exported placeholder obligation by constructing (rp, rn, rx, c1) explicitly as gauge-invariant integrated holonomy inventories on K. We define an edge-surgery “twist” operation whose gauge-invariant content is detected by meridian loop classes and which naturally supports a Z3 primitive (“one-third unit”) without positing fractional point charge as primitive bookkeeping. We give a cluster composition rule for glued 24-cells that preserves gauge invariance and makes boundary-vs-interior cancellation explicit, so the same properties remain meaningful for nuclei. We state explicit falsifiers for gauge non-invariance, failure of YM-form reduction post-@(), failure of Z3 twist detection, failure of composability under gluing, and failure to realize exactly three stable family sectors.