Mathematical Proof of Ontological Uniqueness in Complete Physical Spaces: Theoretical Foundation for 5D Solitonic Unification

We present a rigorous mathematical proof that any complete physical space can admit only one fundamental type of physical law. Through geometric analysis of 5-dimensional manifolds and information-theoretic arguments, we demonstrate that this unique nature must be deterministic. Our theorem provides the theoretical foundation for the 5D solitonic theory developed by A. and N. Copinet [hal-04987740, 2025], establishing it not merely as a possible unification framework, but as the only logically consistent approach to fundamental physics. The apparent coexistence of deterministic (general relativity) and probabilistic (quantum mechanics) laws in 4D emerges as a projection artifact from the complete 5D deterministic reality. We derive explicit conditions for experimental validation and discuss the revolutionary implications for theoretical physics, materials science, and thermal engineering.