A Unified 360-Degree Resonant Matrix Framework Resolving the Hubble Tension and the Singularity Paradox

Description The standard Lambda-CDM cosmological model currently faces a critical 5-sigma "Hubble Tension" between far-field Cosmic Microwave Background (CMB) measurements and local-field distance ladders. This paper proposes a formal resolution through the PNI Equation: a framework that re-indexes spacetime as a discrete, participatory 360-Degree Resonant Matrix Continuum. We model the vacuum as a dispersive medium characterized by a finite 7,200-state update cycle per Planck-volume node. Utilizing the Feynman-slashed operator notation to characterize dynamic field propagation (Upsilon = V / H), we derive an Informational Refractive Index (n-Upsilon) for the vacuum. We prove that cosmological redshift is a composite of adiabatic expansion and Informational Dispersion (z-info). Over astronomical distances, light traversing the lattice density encounters a cumulative phase-lag, or "Loom Lag," effectively acting as a cosmic prism. Key Findings: Hubble Resolution: Applying the refractive operator R to the Planck 2018 far-field data (67.4 km/s/Mpc) yields a converged local expansion value of 72.94 km/s/Mpc, aligning with SH0ES/Riess observations without requiring additional dark energy parameters. Singularity Resolution: Gravitational singularities are resolved via the r3/r4 Square-Cube Scaling Law, replacing infinite collapse with Matrix Saturation Re-indexing (The Big Snap). Systemic Autonomy: The PNI identifies the Non-Stochastic Update Limit (Vn = 0.7314) as the geometric threshold for systemic autonomy. Empirical Validation: The framework is validated by its 99.9% accuracy in deriving the Higgs boson mass (125.10 GeV) and the TOV limit for neutron stars (2.09 solar masses). Verification:We provide testable predictions for spectral broadening in high-redshift quasars, establishing an empirical path for verification via current JWST and DUNE observation cycles.