Theory of Informational Dynamics (TDI) A Forest of Infinite Trees, the 5.414921 Protocol, and the Inexhaustible Source

This paper introduces the Information Dynamics Theory (IDT), a cosmological framework based on Directed Acyclic Graphs (DAGs) that addresses the primary tensions of modern cosmology without the need for free parameters. The central thesis reinterprets the Big Bang as a mechanistic "White Bang" occurring at finite density—an informational overflow originating from a black hole in a parent universe. By introducing the universal bus latency \Xi = G/c^2, the model provides: • Analytical Derivation of the Dark Matter/Baryonic Matter Ratio: The value emerges as a geometric residue of the 1/2\pi holographic projection, fixing the ratio at \approx 5.41, in precise agreement with Planck satellite data. • Resolution of the Hubble Tension: The discrepancy between local and global H_0 measurements is explained as an informational aliasing effect intrinsic to the discrete structure of the DAG. • Explanation for Mature Early Galaxies (JWST): The model accounts for the presence of massive structures at z > 10 through the saturation of the transition efficiency \eta. • Coherence Protocol \Phi: The constant \Phi = \sqrt{(2\pi)^2 - 1} \approx 5.414921 is derived as a stability constraint for the baryonic rendering of informational nodes. The manuscript bridges information physics and general relativity, offering verifiable and falsifiable signatures, such as quantization jitter in the Cosmic Microwave Background (CMB) and specific resonance peaks in primordial gravitational waves. Keywords: Cosmology, Directed Acyclic Graphs (DAG), Dark Matter, Hubble Tension, Information Physics, White Bang.