First-Principles Derivation of Cᵤniv = 1/ (d+1) from Tensor Network Architecture and Spacetime Dimensionality

We derive the universal coherence parameter Cᵤniv = 1/ (d+1) = 1/4 (for d = 3 spatial dimensions) from the dimensional structure of spacetime, independent of any specific tensor network architecture. The key argument is that degrees of freedom partition between the cyclic (temporal) dimension and the d spatial dimensions, yielding Cᵤniv = 1/ (d+1) universally. We verify this result using the HaPPY (Harlow-Pastawski-Preskill-Yoshida) holographic code as a proof of concept, obtaining CᵤnivHaPPY = 0. 20 ± 0. 08 (consistent at <1σ). We prove that global unitarity is preserved across bounces via a unitary rotation in the full Hilbert space, and justify the use of AdS/CFT kinematic structure in cosmological context. This eliminates the last parameter in the framework. Part VII of VII.