The Derived Quadruple: Four Primitive Sectors of Admissible Semantic Transport within the T1–T5 Closure Class

We ask a conditional structural question: if post-onset semantic transportadmits a local, first-order, dissipative, non-chiral, productive closure of type T1–T5, howmany irreducible sectors does its local admissible state possess? Starting from five explicitaxioms on local transport structure, we derive — rather than postulate — a canonicalquadruple Q = (D, h,B, σ) of primitive sectors: a driving field D, a holding capacity h,an internal blockade operator B, and a boundary semipermeability σ. The splitting ofthe transport operator into (σ,B) is not an additional axiom but a canonical theoreminternal to the cone of positive contractions: the operator norm is left adjoint to the scalarinclusion. Within this closure class we prove primitive irreducibility, four categoriallydistinct degeneracy classes, a no-fifth-sector result, non-separability of the natural foldeligibilityfunctional, a no-product theorem for the fold-filtered local theory, and uniquenessof the intervention-separating minimal grammar. We do not prove that T1–T5 is universalacross substrates; cross-substrate universality remains an empirical hypothesis. Thestrongest universal claim established here is therefore conditional: whenever a substrateadmits a T1–T5 closure, the derived quadruple is its canonical minimal local grammar.