Big Bang as a Critical Attractor in a Discrete Pre-Geometric State Space with Emergent Inflation

Proposed is a pre-geometric cosmological framework in which spacetime and inflation emergefrom a discrete graph-based state space. The Big Bang is interpreted not as a temporal singularitybut as a critical attractor (or accumulation point) of a high-dimensional dynamical system definedon network configurations. A coarse-graining procedure yields an effective scalar degree offreedom, identified as an emergent inflaton field. Inflation arises as a relaxation process near adegenerate minimum of an effective potential induced by network connectivity and densityconstraints. The model predicts near scale-invariant perturbations, suppressed tensor modes, andsmall deviations from Gaussian statistics, potentially distinguishable from standard single-fieldinflation.