A Falsifiable Dispersive Signature Test of R-Theory

Paper 1 (R-Theory Recovering General Relativity in the Weak-Field Limit) established a weak-field “equivalence gate”: in the already validated Solar-System regime, R-theory is constrained to reproduce General Relativity (GR) at first post-Newtonian order (PPN γ = β = 1). This paper defines a single, falsifiable extension that preserves that gate yet predicts one new observable: a small frequency-dependent propagation signature in gravitational interaction. The paper is written deliberately in a preregistration style: hypotheses, observables, models, inclusion criteria, and decision rules are declared before running the decisive test to minimize post hoc tuning. The test compares H0 (GR null) ε_d = 0 against H1 (R-dispersive) ε_d ≠ 0 using solar-conjunction geometry, primarily multi-band radio tracking (Doppler and, where available, delay/ranging), with an optional joint radio–optical comparison when suitable mission products exist. The dominant confounder is solar-plasma dispersion, which also produces frequency dependence approximately ∝ 1/f². The pipeline therefore performs conservative plasma calibration by estimating an unknown path-integrated proxy A(t) from multi-frequency differences and subtracting P_f(t) = A(t)/f² (with turbulence allowances), yielding plasma-calibrated residuals r*_f(t). The minimal R-extension is parameterized as c_R(f) = c[1 + ε_d g(f; f0)] with g(f0; f0) = 0, so the model reduces exactly to the GR baseline at a chosen reference band while predicting a differential cross-band effect. Inference is based on a single new amplitude parameter (ε_d), not a flexible curve, and is evaluated via preregistered robustness checks (window/band/station robustness, plasma-model variants, and injection tests). Outcomes are explicitly defined: (A) null → constrain the dispersive extension and report an upper bound on |ε_d|; (B) robust nonzero ε_d → candidate anomaly requiring independent replication; (C) ambiguous → no claim, only limits and required measurement improvements. Open-science commitments include releasing code, configuration hashes, data provenance, and robustness outputs alongside results. Keywords: falsifiability; preregistration; solar conjunction; radio science; dispersion; plasma calibration; Doppler; ranging; Shapiro delay; Bayesian model comparison; robustness checks.