Prose Version - Structural Potentials Under the Persistence Constraint: Gradient Topology, Irreversibility, and Recovery Resistance in the LP Phase Space

This is the prose companion to La Profilée Foundation Series Paper 004 — Structural Potentials Under the Persistence Constraint (DOI: 10.5281/zenodo.20287557). The formal paper derives the topology of the LP phase space: Recovery Narrowing (the contraction of admissible recovery trajectories as IR approaches 1), Structural Hysteresis (path-dependence of structural position), Structural Irreversibility (the existence of a threshold beyond which no admissible recovery trajectory returns), and Topological Completeness. This prose version presents these results as they manifest in real systems: why crises appear to leave no alternatives, why the same IR reading can mean structurally different things depending on trajectory, and why some structural damage cannot be undone.