Axiomatic Foundations of Topological Informational Dynamics

The Axiomatic Foundations of Topological Informational Dynamics (TID) is a non-standard unified theory that synthesizes mathematical physics, metaphysics, and socio-economic systems by positing that physical reality is not fundamentally material, but rather emerges from a timeless, dimensionless, non-conscious substrate known as the Mind-Energy Void. Formalized mathematically as a system composed of a smooth state space, a parameter space, and invariant physical probability measures, TID is governed by five core axioms that integrate information geometry (specifically the Fisher-Rao Metric), ergodic flow, and René Thom’s catastrophe theory. Within this structure, qualitative topological transitions on the parameter manifold are coupled directly to metric divergences. This mathematical framework systematically derives classical mechanics as an informational geodesic minimizing statistical self-differentiation, general relativity as an emergent spacetime statistical manifold shaped by informational entropy and Landauer's Principle, and quantum mechanics as a set of deterministic, phase-shifting transitions and catastrophe-avoidance behaviors operating on a complexified state space.