La Profilée - Structural Closure of the Persistence Domain

The Admissible Reduction Theorem, established in “The Admissible Reduction Theorem” (Paper 65), proves that any persistence condition defined on an LP-admissible system satisfying the structural role constraints reduces to IR = R / (F · I · C) ≤ 1 under reparameterization. The present paper draws the structural consequences of this result. Three corollaries follow directly. First, within D_LP no alternative existence-persistence boundary is structurally possible: any candidate either reduces to IR ≤ 1 or is not a persistence condition in the structural sense. Second, the existence dimension of D_LP is formally closed: the question of which condition governs persistence on the existence dimension has exactly one answer within D_LP. Third, domain-specific persistence theories — across thermodynamics, quantum systems, fluid dynamics, biology, and organisations — are not alternatives to LP but instantiations of IR ≤ 1 in domain-specific variable spaces. These corollaries do not require new proofs beyond Paper 65. They are consequences of a proven theorem. The paper concludes with the closure statement for LP: within the admissible domain, the persistence question on the existence dimension has exactly one structural answer — not because LP defines it that way, but because the structural role constraints of persistence, combined with the uniqueness of the integration capacity form, leave no other option.