Emergence of Z₂ Lattice Dynamics and Topological Defects from Granular Entropic Physics

This paper investigates the emergence of effective field dynamics from a discrete network model of spacetime within Granular Entropic Physics (GEP). Starting from minimal assumptions -- discrete binary degrees of freedom, local interactions, and Z2 symmetry -- the paper shows that the effective dynamics of the GEP network naturally reduces to a Z2 lattice model (Ising Hamiltonian) under these assumptions. This is not a modeling choice but the minimal and natural realization of Z2-invariant local interactions; any other term either breaks Z2 symmetry, involves next-nearest neighbors, or is RG-irrelevant at the critical point. In the continuum limit, the 3D Z2 lattice model yields a scalar phi-4 field theory as the unique result of universality. This is independent of microscopic details and follows from Z2 symmetry and spatial dimension alone. The anomalous dimension of the 3D Ising universality class (eta = 0. 0363, from exact CFT bootstrap) gives a spectral index nₛ = 1 - eta = 0. 9637, consistent with the Planck 2018 CMB measurement of 0. 9649 within 0. 3 sigma, without parameter tuning. The paper further shows that stable topological defects (domain walls in 3D) arise naturally from the double-well potential of the phi-4 theory and are identified as particle-like excitations with Z2 topological charge. Finally, the Clausius relation TdS = deltaQ is derived as a thermodynamic identity from the partition function Z = sum exp (-beta S), not assumed as an independent postulate. The scope is explicitly limited to the minimal dynamical sector of GEP. The paper does not claim to derive gravity, the Standard Model, or exact particle masses. All assumptions are stated explicitly and open problems are identified.