Frustration and Synchronisation on the Tetrahedral Simplex: An Ontological Foundation for Granular Entropic Physics

We propose a minimal ontological foundation for Granular Entropic Physics (GEP) based on a single organising principle: structured tension. We argue that existence entails tension, that tension requires geometric realisation to produce observable structure, and that the tetrahedral simplex (K₄) is the unique minimal frustrated three-dimensional geometry. From the properties of this simplex we argue that the diamond lattice, its Z₂ gauge structure, SU (2) edge holonomies, and chiral symmetry breaking follow as necessary consequences. We propose an inverted vacuum-excitation paradigm in which the ground state is maximally frustrated (zero global phase coherence) and excitations correspond to local synchronisation of nodal phases. Monte Carlo simulations on the frustrated K₄ and on a diamond lattice (N = 216) support this picture: we observe a degenerate ground-state manifold with r = 0, a discrete excitation hierarchy (Delta E in 0, 2, 8), a phase transition with a susceptibility peak at Tc approximately 1. 45 |J|, and systematic energy cost of local synchronisation. We present the complete logical chain as twelve steps from axiom to the Standard Model gauge group and cosmological structure, classify each step by its epistemic status, and identify the open problems that separate the present model from a fundamental theory.