The Recursion-Stability Threshold: A Unified Algorithmic Model for the Emergence of Animate Life

Abstract The origin of life remains one of the most enduring scientific challenges. Existing theories explain aspects of abiogenesis—self-replicating RNA, metabolic networks, mineral templating, or compositional self-organization—yet none provide a unified mechanism for why certain matter becomes animate. This paper proposes the Recursion-Stability Threshold (RST): an algorithmic model stating that life emerges when a material system becomes capable of sustaining a self-referential energy-information loop. Life arises not from rigid crystals nor chaotic fluids, but from semi-crystalline, transformable structures that can simultaneously store pattern, channel energy, deform adaptively, form boundaries, couple to external fields, and amplify recursive processes. When these six conditions converge, matter crosses a critical threshold and becomes proto-life. Drawing on data from biophysics, systems chemistry, mineral catalysis, electromagnetic coherence, and liquid-crystal biology, we demonstrate that RST is the common structural denominator underlying all successful origin-of-life pathways. We conclude by providing an experimentally testable algorithm and outlining a reproducible laboratory pathway for synthetic abiogenesis.