Constrained Inversion of the Admissible Response Function ϕ(x) from the Radial Acceleration Relation

Universal Grid Mechanics (UGM) is an admissibility-first framework in which physical existence is restricted to states satisfying continuity, bounded change, and local information consistency under repeated updates. The frozen UGM02 canon defines the minimal local state X = (S, M). This paper formulates a scoped radial-lane proxy programme for the admissible response law ϕ(x) under current bridge status, operating on the declared radial observational lane and the bounded monotone radial inversion class. Track A and the M0 paper are imported as closed corpus dependencies. The minimal admissible observation-projector scaffold is formalized, licensing radial observable proxies as lawful projection-layer images of admissible canonical response while leaving the unique kernel family, final observation operator, and full projection spectrum open. The pilot uses public RAR point and bin tables (2,693 point rows; 14 binned rows) and a statistically representative reduced Gaia DR3 working table (71,343 rows; 1/250 extraction). The pilot extracts a nontrivial monotone empirical radial observable proxy rising from ≈1.02 at x ≈ −8.9 to ≈8.71 at x ≈ −11.7 over 14 RAR bins. Reduced-Gaia present-epoch Dr values in the inner/mid disk (4.5–8.5 kpc) range from 0.012 to 0.028, consistent with the quasi-steady kinematic assumption. A nonzero present-state angular correction δϕ(x, θ) is not decisively required: independent-sector angular constancy is not rejected at 5% (χ² = 22.76, dof = 14, p = 0.064). The recovered pilot curve is interpreted as an empirical response proxy rather than a final canonical recovery. All uniqueness claims remain conditional on the Hessian positive-definiteness hypothesis of Proposition 9.3.