From Minimal Axioms to Emergent Physics: A Top-Down Derivation of Spacetime Phenomena via the Entropic-Resistance Paradigm

This paper establishes a top-down axiomatic framework for the Entropic-Resistance paradigm, inverting the traditional bottom-up approach of theoretical physics. By defining a minimal mathematical core consisting of five discrete information-theoretic and topological axioms—namely, a dynamic spatial graph, entropic volume updates, topological resistance (volume deficits), recursive relaxation time, and a finite propagation bandwidth (c)—the study demonstrates that macroscopic and microscopic physical laws are not fundamental forces, but necessary geometric constraint reactions. Without ad-hoc parameters, the minimal core top-down derives Newtonian gravity (1/r² displacement), electronic $1/f$ flicker noise, topological superconductivity, relativistic time dilation, and sonoluminescence singularity-avoidance. This framework unifies spacetime phenomena as generative computations of an expanding topological network.