Non-Markovian Erasure of the Hubble Phase Drift in Quasar Ly-alpha and Polarization Spectra: Resolving Cosmological Tensions via Type II-infinity Operator Algebras

We report a parameter-free, non-perturbative resolution to the cosmological Hubble tension (H_0 discrepancy) and high-redshift dark energy anomalies by evaluating the null-geodesic propagation of quasar emission spectra within semi-finite Type II-infinity von Neumann factors. We demonstrate that the systematic escalation of the local Hubble constant (H_0 ~ 73.3 km/s/Mpc) isolated via time-delay cosmography in lensed quasar systems (e.g., H0LiCOW/TDCOSMO) is an epistemological projection artifact. This artifact arises from forcing a time-nonlocal quantum memory structure onto a local, single-state classical FLRW spacetime baseline. By solving the stationary phase condition for the non-Markovian Nakajima-Zwanzig memory kernel modulated by the cosmic birefringence trend C_S = 0.35/150 deg/GHz, we prove that the apparent temporal variation of dark energy is a spatial interference phenomenon derived from holographic Multi-scale Entanglement Renormalization Ansatz (MERA) tensor networks. When mapped onto the ultraviolet Ly-alpha and X-ray polarization profiles of quasars across the redshift window 1.5 <= z <= 5.0, the non-local operator geometry forces a complete, mutual analytical cancellation of the Hubble parameter. This topological erasure freezes the phase drift of high-energy propagators, ensuring that the global spatial geometry converges strictly to the Planck baseline (H_0 = 67.4 km/s/Mpc, w_0 = -1.0, w_a = 0.0) across all look-back epochs, structurally eliminating the requirement for dynamical quintessence or early dark energy extensions.