Identifying Dgal from the MOND Transition

The previous paper in this series connected β, a0, and DGUT through the exact R(Dst)solution and the geodesic equation. This paper derives the exact surplus accelerationformula and identifies Dgal self-consistently. The surplus acceleration from the geodesicequation in the recursion metric is exact: gsurplus = c2R(1 + 2R4)/(6 rH), whererH = c/H0 is the Hubble radius and the (1 + 2R4) factor arises from the full exactODE solution rather than the low-density approximation. The transition conditiongsurplus = a0 gives Rtrans = 0.748 and Dgal/DGUT = 16.79 self-consistently. The densityratio is determined entirely by a0, c, and H0 — three measured quantities. Whatremains is the absolute calibration: the identification of the correct physical definitionof Dst at galactic scales. The definition Dst = ρgal/ρcosmos does not close the gap tothe particle-physics value of DGUT numerically, indicating that Pcontaining for a galaxyin the cosmological hierarchy is not simply the cosmological energy density. This isidentified as the precise remaining step of Open Problem 1.