A Pre-Geometric Framework for Algorithmic Geometrogenesis and Emergent Lorentz Invariance

This compendium establishes a self-consistent, pre-geometric mathematical framework where continuous 4D spacetime, gravitational metrics, gauge fields, and Lorentz invariance are not axiomatic prerequisites but macroscopic emergent properties of an evolving information network. Beginning with a discrete, background-independent native ontology of abstract transaction records, we define a partition function governed by an algebraic graph action. Through an inverse temperature phase transition—Algorithmic Geometrogenesis—the network avoids high-energy ultraviolet (UV) singularities by undergoing dimensional reduction to a $D=2$ structure, while running a renormalization group (RG) flow that exponentially suppresses Lorentz Invariance Violations (LIV) in the infrared (IR) limit. This compendium provides the complete mathematical roadmap, explicit derivations, connections to ultra-high-precision empirical datasets, and rigorous criteria for falsification.