Axiomatic Foundations of The Theory of Us: A Finite-Axiom, Parameter-Free Framework for Emergent Reality

We present a minimal, self-contained axiomatic framework for The Theory of Us—a universal description of physical reality derived entirely from first principles. Starting from the empirically indisputable axiom that “observation impacts reality,” we prove that stable, definite states require two distinct interacting vantage points (dual recognition) and that nature invests only the minimal informational and energetic resources necessary to lock in those states (minimal overhead). By formulating a cost functional for a recognition coverage function and applying variational methods, we rigorously deduce the unique optimal scaling parameter. We then demonstrate that all subsequent physical predictions—ranging from modifications to gravitational field equations to quantum mass generation—emerge uniquely from these finite axioms without any free parameters. Consequently, within its defined domain of observed phenomena, the theory is mathematically closed and, by the Law of Axiomatic Exhaustiveness, fully verified.