Gravity as Stabilized Second-Order Closure: Metricity, Boundary Coherence, and the FRP Real-Carrier Branch

We develop a closure-first framework for gravity in which geometric structure is not postulated at the outset, but appears, when it does, as a stabilized encoding of finite-resolution operational content. Starting from probe classes such as clocks, light exchange, and free-fall comparisons, we define probe-induced closure operators and ask when their stabilized fixed structures admit representation in Finite Resolution Physics (FRP), understood here as a previously developed finite-resolution representational framework. Boundary coherence of such representations requires a dual compatibility-enforcing object, identified with a Simultaneously Interlocked Lagrangian Multiplier (SILM). In regimes admitting invariant-channel decomposition, this object organizes the representational content of the stabilized regime. The central proposal is that gravity corresponds to the existence of a nontrivial second-order closure channel. This is first a statement about stabilized operational relations, not yet about a spacetime field. When such content admits an FRP/SILM representation, it is represented by a rank-2 invariant channel of the relevant automorphism structure. This is the FRP spin-2 sector. The point is not to introduce an artificial spin label, but to obtain the spin-2 sector representation-theoretically before assuming a spacetime geometry; in rigid metric regimes, this sector is the one capable of receiving the usual geometric spin-2 interpretation. Metric gravity is therefore not identified with gravity itself. It arises only when the spin-2 channel satisfies an additional rigidity condition: the existence of a unique nondegenerate invariant pairing preserved under admissible boundary gluing and resolution inheritance. A General-Relativistic description is thereby positioned as a rigid smooth metric realization within a broader space of gravitational closure regimes. The paper does not claim to provide a complete alternative theory of gravity. Its aim is to formulate a structural framework clarifying when gravitational descriptions exist, when they admit metric encoding, and why geometric description should be expected to break down outside sufficiently rigid stabilized regimes.