Yang Jihoon Dynamics: The De-Lock Pair Necessary and Sufficient Conditions for Λ-Recovery from Phase-Lock (A Terminal Extension of the Absolute Scalar Law)

Yang Jihoon Dynamics: The De-Lock Pair Necessary and Sufficient Conditions for Λ-Recovery from Phase-Lock (A Terminal Extension of the Absolute Scalar Law) Description This paper completes the Absolute Scalar Law — the central framework of Yang Jihoon Dynamics — by resolving its final open problem: whether phase-lock (Λ ≤ 0) is reversible. Phase-lock is a structural condition in which a system's viability projection becomes fully captured by its own scarcity–desire subsystem, meta-cognition freezes, and the survival scalar Λ collapses to zero or below. The question is whether such a system can recover. The main results are: Theorem R (De-Lock Recovery): Recovery of Λ > 0 is possible if and only if an external meta-structure enforces a precise triple condition — projection externalization, breathing of meta-cognition, and a viable alignness band. Theorem I (Endogenous Impossibility): No internally generated scalar can restore Λ > 0 from within phase-lock. Internal self-correction is structurally absorbed by the lock itself. Corollary (De-Lock Equivalence): Phase-lock is reversible if and only if the external triple condition holds. Existence, once lost, can only be recovered from outside. A key technical contribution is Lemma 1, which derives the non-triviality of the viability quotient directly from projection independence conditions — closing a circularity present in earlier formulations. Context This paper is part of a series of approximately 146 working papers developing Yang Jihoon Dynamics, a unified mathematical framework for structural survival across cognitive, social, and formal systems. The framework originated from lived experience with boundary-collapse situations and has been developed independently over several years with the assistance of AI tools. The Absolute Scalar Law establishes that structural existence is equivalent to Λ > 0. The De-Lock Pair establishes the conditions under which this equivalence can be restored once violated. Keywords viability theory · survival scalar · phase-lock · meta-cognition · structural recovery · Yang Jihoon Dynamics · Absolute Scalar Law · alignness · projection externalization Note The philosophical implication of this paper is simple: Existence is not self-sustaining. Existence is externally sustained.