La Profilée - The Structural Limits of Persistence: Complete Pair-Collapseability and Complete Non-Collapseability as Boundary Conditions

La Profilée’s foundational papers establish two structural exclusions. Complete Pair-Collapseability (PCP) — the condition in which every state pair can be identified by some admissible transformation — is excluded in LP-EN-ZZ (Determinable Identity under Real Transformation) through the incompatibility of PCP with non-trivial state-coherent identity. Complete Non-Collapseability (CNC) — the condition in which no admissible transformation identifies any two distinct states — is excluded in Paper 50 (La Profilée as a Law of Nature) through the necessity of Module: without non-sink SCCs from which admissible transformations can exit, Assumption 2 (real transformation) is contradicted. The present paper does not re-prove these exclusions. It draws their structural consequence: PCP and CNC are not merely excluded failure modes. They are the boundary conditions that define the LP-admissible domain D_LP from outside. D_LP is exactly the structural space between these two excluded extremes: systems in which identity can be non-trivially constituted (PCP excluded) and transformation non-trivially challenges that identity (CNC excluded). Every persistent system in LP’s sense occupies a position within this space. The structural time variable τ = R / I is substantive precisely within D_LP — because only within D_LP do transformation and identity stand in genuine structural tension.