The Information-Topological Register Model - Cosmological Phenomenology, Falsification Defense, and the Holographic Big Bang

This manuscript constitutes Part VII and the cosmological synthesis of the Information-Topological Register Model. Building upon the discrete mechanical foundations of emergent gravity, quantized mass, and dimensional symmetry breaking (Works 1-6), this paper subjects the theoretical framework to the strict falsification metrics of modern observational astrophysics. Key contributions of this manuscript include: The Vacuum as a Topological Glass: Demonstrating that the discrete vacuum crystallizes as an isotropic Continuous Random Network (CRN) at exactly three dimensions, preventing Lorentz Invariance Violation (LIV) and vacuum birefringence. Wave Kinematics and Fermi-LAT: Applying Effective Medium Theory to resolve the photon dispersion paradox. The model proves that while systematic continuous mean dispersion scales quadratically (E²), stochastic variance (Rayleigh scattering) scales with E⁴ and effectively vanishes. This mathematically aligns with the razor-sharp arrival of high-energy Gamma-Ray Bursts (e. g. , GRB 090510). Absence of Cosmological Defects: Proving that the discrete, graph-theoretic nature of the phase transition fundamentally forbids the generation of domain walls (₀ = 0) and classical continuous monopoles via the Kibble-Zurek mechanism. The Holographic Big Bang: Deducing that the hyper-connected topology of the primordial register (Dₛ) algebraically guarantees a holographic metric collapse where macroscopic time freezes (g₀₀ = 0). The subsequent cooling naturally generates the scale-invariant Harrison-Zel'dovich spectrum (nₛ = 1) for the Cosmic Microwave Background (CMB) without invoking speculative inflationary scalar fields. By distinguishing between continuous fields and discrete graph topologies, this paper establishes a holographically consistent, parameter-free, and testable alternative to the standard model of cosmology.