La Profilée - The Admissible Reduction Theorem

La Profilée’s five Admissibility Requirements AR1–AR5 define the domain of LP-valid system description: systems with an identified identity structure, non-zero structural capacities, definable transformation, temporal extension, and structural coherence between Frame and modules. The present paper proves the Admissible Reduction Theorem: any persistence condition defined on an LP-admissible system is either equivalent to IR = R / (F · I · C) ≤ 1 under reparameterization, or it is not a persistence condition in the structural sense. The proof proceeds in three steps. First, we show that AR1–AR5 jointly force a specific variable structure on any persistence condition defined within the admissible domain: the condition must contain a transformation component and an integration capacity component, and these must be relationally structured. Second, we show that the Functional Uniqueness Theorem — established in “La Profilée as a Law of Nature” — uniquely determines the form of the integration capacity component as F · I · C within the admissible domain. Third, we show that any relational persistence condition with this variable structure is equivalent to IR ≤ 1 under reparameterization. The result closes the admissible domain: within LP’s structural universe, no alternative persistence condition exists.