The Architecture of Reality: A Mathematical Framework for Emergent Organization, Structural Memory, and Space-Time Geometry

The Architecture of Reality: Equilibrium, Structural Memory, and the Origin of Universes presents a mathematical framework in which spacetime, gauge interactions, and matter emerge from localized departures from a primordial equilibrium state. The theory introduces two fundamental organizational variables—Structural Coherence (Q) and Structural Memory (M)—and develops their evolution using tools from gauge theory, Einstein–Cartan geometry, sheaf theory, algebraic topology, and adelic geometry. The framework derives emergent gauge fields, organizational stress-energy, spin density, and spacetime torsion within a unified mathematical structure while remaining compatible with General Relativity in the appropriate classical limit. It also proposes falsifiable observational predictions, including gravitational-wave echo signatures and topological persistence thresholds, providing explicit pathways for experimental testing. This Version 2.0 represents the first complete mathematical formulation of the framework intended for public dissemination and future peer-reviewed journal submission.