UNIFIED EXISTENCE FRAMEWORK Formal Extension of Geometric Information Tunneling

Abstract

The Unified Existence Framework Geometric Extension (UEF-G) established the mathematical foundations of information tunneling as a non-local correlation mechanism within the geometric axis Γ of the infinite potential field P∞. The present document constitutes a formal companion to the frozen UEF-G baseline, addressing each item identified in the Revision and Development Guidance without modifying the original record. Specifically, we provide: (1) a rigorous differentialgeometric definition of P∞ as a structured manifold tuple; (2) a fiber bundle formulation of the projection operator π : Γ → M ₄ ; (3) a complete dimensional analysis of all field quantities; (4) a formal terminology mapping that preserves UEF canonical terms while introducing scientific aliases; (5) Lyapunov-based stability analysis of the disturbance propagation equation; (6) topological formalization of the toroidal synchronization mechanism; and (7) explicit falsifiability criteria. The central result is a formal proof that information tunneling is geometrically possible within UEF — not merely conceptually consistent, but structurally entailed by the framework's axioms and the differential geometry of Γ.