The Informational-Quantum Paradigm of the Cosmological Cycle: Axiomatic Scale-Norming of the Pregeometric Network and the Entanglement-Density Nature of Gravitation and Mass

[Update Aug 2026]: Paradigm v9.0 added, featuring 5D Extended Sokolov Tensor and Core Operator classification.[Update July 2026]: Paradigm v8.0, incorporating Triple Cross-Scale Verification and Cognitive Mining Law.[Update July 14, 2026]: Paradigm v6.0, introducing QFT mass matrices, Perelman's surgery, and JWST solutions. This manuscript details "Timeless Informational Realism," proposing an emergent framework where spacetime and gravity originate from a Primary Quantum-Information Register (R₀) and Pregeometric Network. Key derivations include identifying Newton’s G as a macro-scaling factor and spatial pixelation via the Sokolov Algebraic Volume Invariant. The work establishes a c-phase-refresh limit, derives kB from background entropy, and applies the Sokolov Isomorphic Projector for matter field derivation via Functional Renormalization Group methods. Global connectivity is analyzed via Category-theoretic Functors and the Sokolov Spherical Web Trace Identity, establishing a 5D "eternal Now" and addressing the 10¹²⁰ cosmological constant paradox through algorithmic compression and conformal invariance.