Gravity-Like Spatial Deformation and Inverse-Square Behavior Emerging from Relational Reaction Structures: A Structural Consistency Test Against Gravitational Signatures

This study tests whether the relational universe structure derived in preceding stages is structurally compatible with nontrivial signatures of known gravity. Gravity is selected as a stringent consistency test without presupposing either a complete fundamental reconstruction of gravity or identity with the gravitational sector of the observed universe. The preceding development established a deterministic reaction on canonical cores, exact dyadic subdivision in a clean sector, an S2-fibered three-dimensional spatial total space, a reaction-indexed four-dimensional world-volume, and 54,180 primitive recurrent rooted rays. The central structural input used here is the contrast between the exact recurrent fixed-even two-step law dt+2=dt and the clean-sector law Lt+2=4Lt. Consequently, for the dimensionless reaction-scale diagnostic t=dt/Lt, one has t+2=t/4. Recurrent persistence therefore leaves a nonvanishing deformation deficit relative to clean growth. The local census of the generated recurrent system yields the exact central excess Nx=35+x0 in each relevant K7 cell. The Laplacian spectrum of B0 and the spectrum of the Johnson graph J7,4 underlying the K6 parent-source space are also closed by exact finite calculation. Up to this stage, no metric, Lorentzian signature, Poisson equation, or Newtonian force law is assumed. The derived structure is then transferred to a continuum metric representation for an internal 3+1 observer and compared with known gravitational signatures. This is an explicit correspondence layer, distinct from the structural theorems. Under the zero-shift 3+1 convention fixed in this paper, a frame-covariant deformation tensor occupies the same mathematical position as the mixed tidal-curvature block. For a localized recurrent anomaly, the graph-Laplacian pseudoinverse response has a 1/4r Green singularity in a regular three-dimensional continuum regime; when the C2 source map and C3 motion correspondence are applied, its gradient produces an inward 1/r2 response. A quadratic source-response functional with >0 is also non-positive, although that sign alone is not interpreted as an independent proof of pairwise attraction. The claim of this paper is therefore not that the gravity of our universe has been completely proved. Rather, in the verified relational sector, a clean/recurrent deformation deficit, a local source-like excess, a tidal-curvature correspondence, a non-positive quadratic source-response sign, and a local three-dimensional inverse-square inward response arise within one coherent construction. The result is a consistency test showing that the previously derived universe structure can exhibit nontrivial structural compatibility with known gravitational signatures. It does not claim the full Einstein dynamics, an exact lensing coefficient, absolute SI values of observed constants, or complete identity with the gravitational sector of the observed universe.