The Phase Space of Persistent Systems: A Universal Morphology of Persistence Under Transformation

Paper 000 derived the minimal admissibility architecture of determinate persistence under real transformation. Paper 001 established that every real persistent system instantiates this architecture and that LP is structurally identical to F₀. The present paper derives the next consequence: if LP is the universal structural architecture of persistent reality, then the space of possible persistent systems cannot be arbitrary. Their admissible forms, transition paths, and boundary regimes must themselves be structurally constrained. This paper derives the LP phase space: the universal structural morphology of persistence-capable systems. The paper establishes four results: First, the primary structural coordinates of the phase space are the LP variables themselves — Frame, Module, Coupling, transformation load, identity drift, and successor orientation. These are not imposed from outside. They are generated by the persistence architecture of Paper 000. Second, a set of derived coordinates — reserve, fragility, drift rate — are shown to be functions of the primary variables, not independent dimensions. Third, the admissible regions of the phase space correspond exactly to the six universal sub-regimes established in Paper 000. No additional regions exist. Several combinations are structurally forbidden. Fourth, the transition rules governing movement between regions follow from the LP architecture without additional premises. The claim is not that all persistent systems are identical. The claim is: all persistent systems occupy positions within the same structurally constrained phase space. LP does not generate a periodic table of discrete substances. It generates a phase space of persistence, with structurally forced regions, forbidden zones, and admissible transition paths. Methodological Note on Claim Classification This paper adopts the four-tier classification established in Paper 000: Theorem (Class A): formally derivable. Structural Consequence (Class B): forced under stated conditions. Interpretive Corollary (Class C): conceptual identification. Ontological Consequence (Class C): scope statement.