Emergence of the Standard Model from Spacetime Optimization: Topological Motif Mining in the QGEFT Framework

The current Paper 56 benchmark does not claim that the full experimental Standard Model has already been derived from first principles on a graph. It does show that, in the verified late-time `N=64`, `1000`-sweep guided Topological Twins branch, a sharp hierarchy of topological motif lifetimes emerges automatically. The sparse `path-4` motif dominates the cold window with `40812` tracked lifetimes and a longest survival of `48/51` frames, while the densest `tetrahedron` sector appears only once and survives for exactly `1` frame. Intermediate motifs (`tailed-triangle`, `cycle-4`, `diamond`) occupy the expected middle ground of abundance and stability. The defensible conclusion is therefore that QGEFT cooling already selects a particle-like hierarchy in which low-stress sparse structures are thermodynamically favored and ultra-dense heavy sectors are strongly suppressed.