The Constitutive Gravitational Framework VII: A Dimensional No Go Theorem for the Spherical Casimir Origin of the Infrared Normalization, and the Surface Term Route Toward a Unified Action

In Paper V of this series the deep-MOND infrared branch of the constitutive response function was traced to a spherical Casimir-like surface energy of the gravitational vacuum, giving the action branch F_IR = F₀ Y³ᐟ² with the normalization F₀ left undetermined; Paper VI fitted F₀ = 0.777 empirically from the Radial Acceleration Relation. The present paper completes the surface-to-volume embedding that Paper V deferred and proves that it cannot supply F₀. The obstruction is dimensional, not numerical. The single-sphere Casimir energy of a scalar field whose only length is the boundary radius L is E_C = α_s ℏc / L, an energy that, read through the spherical geometry, is a surface density (J m⁻²), whereas the covariant action term is a volume density (J m⁻³). Mapping one into the other requires a fixed length d, and solving the embedding for the observed F₀ = 2/3 forces d ≈ 8 × 10⁻⁹⁸ m, roughly sixty orders of magnitude below the Planck length and therefore not a physical length in any effective field theory. We show that the energy-density ratio ℛ ~ 10⁹⁵ quoted in Paper VI is itself the numerical signature of this missing power of length, and that no dimensionless effective mode count N_eff can restore it: bridging the gap by mode multiplicity alone would require N_eff ~ 10⁹⁷, i.e. an angular cutoff ℓ_max ~ 10⁴⁹, some sixty orders above any sub-Planck spherical-harmonic cutoff. We conclude that the spherical-Casimir mechanism supplies the infrared SIGN (repulsive, matching ρ_x = 2ρ_vac) and the infrared POWER (Y³ᐟ²), but not the COEFFICIENT, which is purely kinematic (F₀ = 2/3 is the reciprocal of the integration exponent and carries no Casimir content) and must be fixed empirically. We then show that the minimal action structure able to host a genuine surface density without an unphysical d is a boundary/non-local term, and we make explicit that such a term RELOCATES the normalization into a new dimensionful coupling rather than removing it — identifying precisely the object a future unified action must determine from data. The finite-mode (level) structure of earlier papers is retained, but in its dimensionally admissible role: setting the SHAPE and weak-to-strong transition scale of the response, not its absolute normalization.