R-Theory Recovering General Relativity in the Weak-Field Limit

General Relativity (GR) is experimentally dominant in the weak-field regime, so any alternative framework must first reproduce the classical Solar-System tests before proposing novelty. This paper presents R-theory, a resonance-based field interpretation built around a coherent background (“zero field”) and phase-coupled dynamics. Under a minimal, explicitly stated mapping from R-variables to operational observables, we show that R-theory recovers the standard first post-Newtonian (1PN) phenomenology of GR for: (i) Mercury’s perihelion advance, (ii) leading-order light deflection, (iii) Shapiro time delay, and (iv) gravitational redshift. Crucially, the mapping is anchored in the standard PPN language and a compact “gate necessity” argument is provided: under weak-field universality, local Lorentz invariance, and a single coherence-factor coupling to matter and radiation, the gate coefficients are fixed globally rather than tuned per dataset. Weak-field equivalence is treated as a consistency gate (not as evidence against GR). The result is a clean baseline from which a follow-up work can introduce a preregistered, genuinely falsifiable discriminant signature (Paper 2) without altering the equivalence constraints established here. This combined version includes a derivation-friendly effective-metric construction (WKB and Poisson limits) and outlines a minimally invasive, frequency-sensitive discriminant direction using Cassini solar-conjunction radio science. Keywords: weak-field gravity; post-Newtonian limit; PPN; perihelion precession; light deflection; Shapiro delay; redshift; resonance; phase-coherence; effective metric; Cassini radio science.