From Relational Resolution to Unified Physics: The Fidelity Function across Fourteen Sectors

Relational Resolution Theory (RRT) extends Landauer's principle to a relational ontology with five axioms (A1–A5) governing format, resolution, translation, proper time, and relational distance. Relational Substrate Theory (RST) applies RRT to the physical universe and derives a fidelity function μ (η, n) = η/ (1+ηⁿ) ^ (1/n) from the requirement that signal and noise share a finite budget. The Resource Triangle is Wⁿ = Ωⁿ + Nⁿ; the main equation is I = Ω·μ. The exponent n (transition sharpness) varies by sector and is interpreted as the Hausdorff dimension of the relational pathway. This paper reports calibrations across fourteen sectors: gravity (SPARC, n=1. 25, ~86% acceptance), tensile stress–strain (30 materials), electrical resistivity (15 metals), thermal conductivity (15 metals), fluid viscosity (12 fluids), dynamical friction, magnetic hysteresis (8 materials), and Standard Model running couplings (n=1, 3, 8 from gauge generators). Five mathematical identities are exact (R²=1): the Lorentz factor at n=2, the particle-in-a-box spectrum, the hydrogen atom spectrum, the Michaelis-Menten equation at n=1, and the Hill dose-response equation as μⁿ for all n. Starting from a single empirical input (n=1. 25, calibrated against SPARC), the Sovereign Chain derives the Weinberg angle, fine-structure constant, muon/electron and tau/electron mass ratios, proton/electron mass ratio, and the Z boson and top quark masses—all within <0. 07% of measured values. No parameters are fitted to particle physics data. The theory makes a falsifiable prediction (Gate 1): at redshift z=2, flat rotation velocities should be ~31% higher than at z=0 for fixed baryonic mass—testable with JWST/ALMA. RST does not claim zero free parameters or a Theory of Everything. Full development (relational vault, code, Reality Engine ledger simulator) is linked from the paper. This work has not been peer reviewed.