La Profilée - Derived Structural Categories: On the Necessary Structural Consequences of Restricted Transformability

Paper 103 establishes that any system admitting distinguishable states (C1), real transformation (C2), and determinate persistence verdicts (C3) must be non-transitive under admissible transformation. Restricted transformability is therefore not optional — it is forced by the persistence problem itself. This paper proves that a set of structural categories is not optional under this condition. Each is derived by contradiction: its negation destroys either persistence determinacy, the admissibility of transformation, or the non-triviality of the induced reachability structure. The categories established: partial order on identity classes, asymmetric structural dependence, strict contraction of reachable futures, absence of inverse reachability, and irreversible future-selection. A minimality theorem shows that each is individually necessary: removing any one collapses the persistence structure.