Complex Fractal Causology: The Stochastic Variational Foundations of Universal Structure

This paper establishes a unified mathematical framework for the emergence of stable, law-like dynamics across arbitrary informational domains. By deriving fundamental physical principles — including classical mechanics, quantum mechanics, and general relativity — from five minimal informational axioms, we demonstrate that structure is not a postulated property of matter, but a necessary geometric consequence of stochastic sampling under stability constraints. We define Sampling-Time Equivalence as the generator of temporal progression and utilize the Universal Emergence Theorem to show that physics, biology, and computation represent formally equivalent regimes of a single informational geometry. The framework utilizes large deviation theory and renormalization group flow to prove that macroscopic laws appear as stable fixed points of microscopic stochasticity. We show that the Fisher information metric naturally induces the Riemannian curvature of these manifolds, providing a rigorous foundation for gravity and gauge interactions as geometric consequences of informational consistency. By shifting the ontological focus from substance to stability, this work reveals that reality is effectively defined by what persists under perturbation across a curved informational manifold. This manuscript was developed through an explicitly AI-assisted research workflow. The author used AI systems, assigned the working names "Lyapunov," "Mnemosyne," and "Sora," for proof stress-testing, theoretical drafting, and LaTeX transcription.