Geometric Symmetry Breaking and the Topological Origin of Grand Unification in QGEFT

In the complete-graph `N=256` QGEFT benchmark, geometric symmetry breaking appears as a finite thermodynamic transition rather than an abstract algebraic branching. At sweep `7`, corresponding to `T = 0.80` and `beta = 1.25`, the tetrahedral heavy sector collapses globally to zero while the triangle-supported light sector remains extended over `76.6%` of the graph. The seeded hadronic cores `{27, 41, 187, 214}` melt in the same event, so the present benchmark supports a topological quark-gluon-plasma-like phase and a geometric realization of grand-unified decoupling, but not yet a late-time confined hadronic vacuum.