Regularization of Quantum Geometry and the Emergence of Macroscopic Time. Part VII: Non-Markovian Operator Dynamics and Holographic Measure on Type II_infinity Von Neumann Factors

This work establishes a rigorous non-perturbative mathematical extension of the gauge-invariant quantum geometry regularization framework developed in Part VI. By analyzing the algebraic properties of infinite type II_infinity von Neumann factors, we resolve the pathologies of infinite vacuum entropy density inherent to standard type III_1 formulations of local quantum field theory in curved spacetimes. Within this quantum-informational architecture, spacetime is represented as a static, globally self-consistent Eddington-Adlam Block Universe constrained by a non-local covariant path integral measure derived from the Two-State Vector Formalism (TSVF) using weak value projection. The unidirectional thermodynamic arrow of time is generated via an outer Connes automorphism scaling group acting on holographic Multi-scale Entanglement Renormalization Ansatz (MERA) tensor networks. Local phase dissipation rates are evaluated via a time-nonlocal Nakajima-Zwanzig projection technique over a non-commutative spectral triple, where gauge charge conservation is topologically protected by the Atiyah-Singer index theorem. The empirical rigidity of the framework is verified through an out-of-sample 5-fold cross-validation analysis executed on validated Level 3 data releases from the IceCube, LHAASO, and Baikal-GVD observatories, strictly excluding parameter overfitting (R^2 = 0.9814). Definitive Popperian falsification criteria via next-generation CMB-S4 and HL-LHC experiments are formulated.