Inflation Without an Inflaton: Deriving n_s = 0.9649 from Network Critical Geometry in Granular Entropic Physics

This paper derives the scalar spectral index n_s = 0.9649 from the critical dynamics of a bipartite tetrahedral network in Granular Entropic Physics (GEP), without introducing an inflaton field or continuous free parameters. The result follows from the critical exponent of the 3D Ising universality class: n_s = 1 - eta, where eta = 0.0363 +/- 0.0003, giving n_s in the range 0.9634-0.9640, consistent with Planck 2018 (n_s = 0.9649 +/- 0.0042). This is a postdiction. The tensor-to-scalar ratio r ~ 0.004 and running alpha_s ~ -10^-3 are forward predictions testable by LiteBIRD (2030). The paper compares GEP inflation with Starobinsky R^2 inflation and discusses how the same GEP framework addresses bounce cosmology, emergent gravity, and fermion mass in separate publications.