Where R-Theory Deviates: Falsifiable Predictions of Phase-Potential Gravity

Where R-Theory Deviates: Falsifiable Predictions of Phase-Potential Gravity Even if Papers 1 and 2 are fully consistent with weak-field General Relativity, a critical question remains: is the phase-potential framework more than a relabeling of GR? This paper addresses that question directly by defining a controlled, explicitly falsifiable deviation space. Three deviation channels are introduced: (A) modified coupling of clocks, matter, and light to ψ (PPN-like parameters), (B) extensions of the ψ field dynamics (e.g. Yukawa scale, dispersion, nonlocality), and (C) nonlinear self-energy effects in stronger fields. Each channel is tied to concrete experimental and observational programs, including precision clocks, laser and atom interferometry, satellite dynamics, and strong-field astrophysical systems. The emphasis is on minimal parametrization and measurement routes rather than speculative claims. This paper is intentionally conservative in tone: it defines where deviations could appear and how they can be bounded or ruled out by data. The framework stands or falls by this deviation budget. Series context: • Builds on the weak-field skeleton of Paper 1 and the covariant structure of Paper 2. • Supplies the deviation parameters that are translated into phase signatures in Paper 4.