A kinetic-conformal two-role completion of the radial acceleration relation

The radial acceleration relation (RAR) of galaxies admits a quasi-linear nonrelativistic description (QUMOND). We address the more restrictive target of a relativistic completion that simultaneously secures the lensing–dynamics relation, freedom from extra propagating modes, positive admitted energy, solar-system limits, and a cosmological endpoint. We construct a covariant action for one physical metric g_μν, a khronon field T defining a preferred foliation, and a nonpropagating auxiliary potential φ_N, with matter coupled minimally and universally to g_μν alone. A coefficient-locked square completion makes the weak-field no-slip condition Ψ=Φ an equation of motion and assigns the Newtonian source exactly once, while the static limit reproduces the QUMOND system exactly. At the kinetic-conformal point the trace of the extrinsic curvature becomes a primary constraint. On the declared finite, matched, weak-field branch — including the nonlinear bulk constraints and the small-background inverse gate — we verify closure of the constraint algebra with two tensor modes and no propagating scalar, positivity of the admitted quadratic energy under the stated finite spectral inequalities, and on the exact affine high-acceleration branch the standard khronometric weak-field dictionary maps the first post-Newtonian parameters to their general-relativity values, with finite-profile observables deforming continuously under a finite bound. On a separate branch — homogeneous, fixed topology, harmonic zero mode — a coefficient-locked volume-summary completion, implemented by an auxiliary scalar pair (ϑ, b) that restores one global volume canonical pair, recovers the standard Friedmann equations exactly; the time-dependent junction between the two branches remains open. The scope of every statement, and the items deliberately left open (profile origin, interface normalization, transient and strong-field completion, branch junction, empirical confirmation), are stated explicitly. This is the theory companion of the jointly released Letter "A conditional horizon-readout prediction for the galactic acceleration scale and its SPARC test" (doi:10.5281/zenodo.21423446). Preprint version v0.6.2; submitted to Physical Review D.