Persistence Dynamics: Structural Trajectories, Attractors, and Instability Basins in the LP Phase Space

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. Paper 002 derived the LP phase space: the universal morphology of persistence-capable systems, including admissible regions, forbidden regions, the Coherence Zone, and structurally constrained transition paths. The present paper derives the dynamics of that phase space. Persistent systems do not merely occupy positions in the LP phase space. They move through it. The question is whether this movement is arbitrary or structurally constrained. The answer is the latter: LP's admissibility conditions generate a gradient structure in the phase space that constrains all admissible persistence trajectories from within. The central result of this paper is a structural dynamics theorem: real transformation under LP admissibility conditions necessarily generates directed, constrained trajectories. The LP architecture does not merely describe where systems can be — it generates the admissibility gradients that govern how they move. Five further consequences follow from this foundation. First, persistent systems trace structurally admissible trajectories through the LP phase space, constrained by the Coherence Zone. Second, LP's admissibility gradient produces a position-dependent amplification of transformation consequences — the same perturbation has structurally different effects depending on proximity to the Coherence Zone boundary. Third, Flourishing and Fragile Persistence are not merely labels but structurally distinct dynamical regimes with opposite gradient orientations. Fourth, the LP architecture generates structural asymmetry between degradation and recovery: degradation occupies a broader admissible trajectory space than recovery. Fifth, Directed Transmutation is structurally interpretable as a Coherence Zone transition — the organized movement from one stability region to another. The dynamics of persistent reality are not externally imposed on LP structure. They are generated by it.