Stabilization Dynamics for Life Emergence - A Technical Formulation within the ψ₀-OCM.pdf

This paper presents a technical framework for life emergence based on stabilization dynamics, rather than chance assembly or fine tuning. A minimal set of effective fields is introduced to describe (i) continuous energy–information throughput, (ii) boundary constraints that regulate this throughput, and (iii) persistence against destabilizing influences. From these ingredients, a stability criterion is derived that specifies when structured systems can remain long-lived rather than rapidly decaying. This criterion is formulated through sufficient inequalities that guarantee positive invariance—once stabilized (denoted in the ψ₀-OCM as a persistent PDS-1 state), the system does not spontaneously collapse—and Lyapunov-type stability, meaning that small perturbations do not destroy persistence. Under sustained stabilization and bounded destabilization, an internal coherence measure is shown to converge toward a non-zero steady state, indicating persistent organization far from equilibrium. Within this regime, adaptive feedback emerges generically as an attractor property of the dynamics, rather than as a finely tuned or exceptional mechanism. The result is a closed, internally complete mathematical scaffold that can be calibrated and specialized for applications in astrophysical, planetary, and biological systems, without assuming specific chemistry, environments, or microscopic implementations.