Gravity as Vacuum Relaxation: D8 Geometry as the Ultraviolet Completion of a Unified Framework

Building upon the earlier "Damped Vacuum Relaxation Theory of Gravity" (DVRT) framework, this paper proposes its ultraviolet completion: the eight-dimensional demi-cube D8 geometry. We prove that the dynamics of the scalar field φ, the density screening mechanism, the galactic rotation curve correction coefficient α ≈ 3/8, and the CMB scale-separation argument in the DVRT framework can all be derived from first principles of D8 discrete geometry, without introducing any free fitting parameters. Specifically: (1) The vertex count 256, eigenvalue spectrum \{8-2k|k=0,…,8\}, and automorphism group of order 2^8· 8! constitute the discrete vacuum ground state of the D8 geometry; (2) The projection ratio from D8 to the three-dimensional observer space is rigidly fixed at 3/8, directly corresponding to the galactic fitting correction coefficient α in the DVRT framework; (3) The eightfold symmetry of D8 rigidly fixes the projection angle to π/8, whose sine sin(π/8)=0.382683 agrees with the lattice QCD vacuum multifractal minimal singularity exponent, the algebraic K-theory generator, and the topological S^7 parallelisation parameter, forming a sevenfold consistency verification; (4) In the infrared limit, the renormalisation-group flow of D8 drives the effective dimensionality from 8 down to 4, automatically recovering Einstein gravity and the Bekenstein-Hawking entropy formula. We provide a complete mapping dictionary from D8 to DVRT, the derivation of the action, spectral analysis, RG flow equations, black hole entropy calculations, and three testable predictions. This framework starts from the single axiom "vacuum = D8 discrete geometry" and unifies galactic dynamics, gravitational wave speed, CMB compatibility, black hole entropy, QCD vacuum structure, and several geometric constants from algebra and topology, all with zero free parameters.