A Unified Logical Foundation for Gauge Theory, Quantum Mechanics, and General Relativity from Reference Frame Self-Consistency

The three pillars of fundamental physics—quantum mechanics, gauge field theory, and general relativity—each rest on axiomatically independent foundations. We argue that this independence is a product of historical contingency rather than logical necessity, and we propose that a single principle, Reference-Frame Self-Consistency (RCC), underpins all three sectors. Starting from a bare state-space manifold carrying no preordained linear structure, metric, or inner product, RCC demands that physical laws be formulated independently of any arbitrary choice of local reference frame; the central mathematical object that enforces this requirement is the nonlinear comparator Γ—a G-equivariant diffeomorphism between state-space fibres. Constrained solely by G-equivariance, the comparator’s consistency evolution equation uniquely yields (i) the generalized Born rule as the G-invariant transition function, (ii) the Yang-Mills action as the flat-geometry limit of the comparator invariant, and (iii) the Einstein-Hilbert action from the fibrewise geometry in the classical long-wavelength limit. Crucially, the nonlinear framework predicts corrections beyond each standard pillar that are not optional extensions but direct requirements of self-consistency: a fibre-phase gauge field κµ and its kinetic mixing with the Standard Model hypercharge boson Bµ, and SMEFT Wilson coefficients controlled by a single geometric scale k∇ϑk 2 with coefficient ratios uniquely fixed by the group-theoretic Dynkin indices. We further prove a Phase Unification Theorem: the three structures of comparator ambiguity, nonlinear connection holonomy, and the centre-group action on the state space are mutually isomorphic, providing the geometric origin of κµ. On the experimental side, we construct a nested hypothesis-testing framework (Kähler limit H0 vs. nonlinear H1) and an experimental roadmap spanning from LHC Run 3 to FCC-ee. Departures from the standard Born rule beyond the Kähler limit and sub-leading gravitational corrections parametrized by the fibre curvature scale collectively constitute a comprehensive set of falsifiable predictions accessible to collider, quantum-optical, and cosmological probes.