Gravity as a Response Law: An Admissibility Projector on Physical States

This paper proposes a reinterpretation of gravitation as a global response law rather than a force law. In this framework, local degrees of freedom do not interact via forces; instead, they respond under a global constraint, and only those responses that remain admissible persist. The central mathematical object is an admissibility projector, which selects globally coherent responses from the space defined by a fixed response operator. The paper distinguishes clearly between three layers: (i) a universal response operator that defines possible modes, (ii) its Green’s function (the kernel) as a representation-dependent response map, and (iii) an admissibility projector that enforces global coherence and topology, determining which responses can persist. Local force laws, including Newtonian gravity and general relativity, are shown to arise as linearizations of motion within the admissible response subspace. This framework unifies empirical regularities across disparate domains, including galaxy rotation curves, wide binaries, protein folding, and biological polarity, without introducing new particles, forces, or per-system tuning. As an empirical demonstration, the paper presents a new analysis of the SPARC rotation-curve database, showing that the observed radial acceleration relation emerges naturally from the response-law framework: extended non-local response is admitted in the weak-field regime and collapses smoothly to Newtonian behavior at high baryonic acceleration. The work makes explicit, falsifiable predictions and is intended as a foundational preprint. It has not yet undergone journal peer review.