Symmetry, Entropy, and Fractals: A Noetherian Framework for the Unfolding of Persistence

We propose a conceptual and mathematical framework linking symmetry, entropy and fractal geometry by introducing the Axiom of One: every instance of persistence(a negation of the vacuum) is represented as one. We show that scale invariance via Noether’s theorem, implies fractal self-similarity, and that entropy is the logarithmic measure of fractal branching. Symmetry breaking increases entropy by expanding phase space while preserving ontological unity. This framework unites physical symmetry principles with the geometry of entropy and provides a new perspective on the mathematical structure of physical law.