The Information-Topological Register Model

This work introduces the Information-Topological Register Model, a discrete, deterministic framework that replaces the continuous spacetime manifold with an amorphous Continuous Random Network (CRN). By postulating that physical reality emerges solely from the thermodynamic relaxation of logical graphs, this model analytically derives General Relativity and Quantum Mechanics as macroscopic projections of the same underlying network tension. We demonstrate that matter is not an independent substance, but a topologically stabilized 1D-knot (e.g., a trefoil) within the 3D vacuum, providing a geometric solution to the Yang-Mills mass gap. The model successfully derives the fine-structure constant (α ≈ 1/137) via 3D combinatorics, calculates the primordial spectral index (ns ≈ 0.96) from topological vacuum friction, and analytically predicts the baryonic matter density (Ωb ≈ 4.74%) as the absolute percolation limit of the vacuum graph. Furthermore, we unify gravity, electromagnetism, and dark energy strictly through the Helmholtz-Hodge decomposition of the network's topological stress. The paper concludes by proposing specific, high-precision falsification experiments, including macroscopic BEC-interferometry to test violations of the Weak Equivalence Principle.