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 ($E^2$), stochastic variance (Rayleigh scattering) scales with $E^4$ 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 ($\pi_0 = 0$) and classical continuous monopoles via the Kibble-Zurek mechanism.
• The Holographic Big Bang: Deducing that the hyper-connected topology of the primordial register ($D_s \to \infty$) algebraically guarantees a holographic metric collapse where macroscopic time freezes ($g_{00} = 0$). The subsequent cooling naturally generates the scale-invariant Harrison-Zel'dovich spectrum ($n_s = 1$) 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.