La Profilée - Collapse-Recovery Asymmetry: A Structural Law of Irreversible Time in Persistent Systems

This paper derives the Collapse-Recovery Asymmetry as a universal structural law: for any system that maintains persistent non-trivial identity under real transformation, T_col < T_rec strictly, and the time-reverse of a collapse process is structurally inadmissible. The result is universal, not model-dependent. Its universality rests on a complete three-step chain: (1) Paper 52 proves that any system with persistent non-trivial identity under real transformation necessarily instantiates the LP structural architecture — from minimal conditions (distinguishable states, real transformation, non-trivial invariant identity), the Frame-Module-Coupling decomposition and the persistence condition IR = R / (F · I · C) ≤ 1 are forced, without any invariance assumption; (2) this persistence condition admits a unique representation (Papers 33, 50); (3) the present paper derives the asymmetry as a necessary consequence of this structure. The asymmetry is therefore not a consequence of LP as a model. It is a consequence of what it means for a system to have identity at all. The asymmetry is forced by two structural facts that cannot be simultaneously absent in any LP-admissible system: collapse is parallel and amplifying — degradation phases overlap (Corollary to Lemma 2) and drive each other (Lemma 1); recovery is serial and non-amplifying — no two restitution stages can overlap in durable effect (Corollary to Lemma 3) and no stage accelerates the next (Lemma 4). Four alternatives are excluded: serial collapse, parallel recovery, recovery amplification, and T_rec/T_col approaching 1. Three structural corollaries follow: physical irreversibility for LP-governed systems (Corollary 3); strict irreversibility of coupling after any non-degenerate episode (Corollary 1); and monotonic fragility under repeated collapse (Corollary 2). The final claim: structure fails in parallel. It must be rebuilt in order.