Finite Relational Quantum Gravity: From Axiomatic Foundations to Cosmological, Holographic, and Information-Theoretic Consequences

This paper describes the complete foundational theory and physical consequences of Finite Relational Quantum Gravity (FRQG). Starting with two principles, Bounded discreteness and local relational symmetry, this paper provides mathematical proofs deriving: Non-Ableian Gauge Fields and Yang-Mills Action, Emergent Relational Time and (3+1)D Lorentzian Signature, General Relativity as an Emergent Limit, Hologrpahy and Unitary Black Hole Evaoporation, Cosmological Bounce and Unimodular Dark Energy, and Phenomenology and Evasion of No-Go Theorems.