Triangulated Inevitability of Deterministic Admissibility Architecture: Requisite Variety, Supervisory Control and Enforcement, and the Generator–Supervisor Decomposition of Complete Intelligence

Abstract

This paper isolates and externally triangulates one architectural result of the Scope–Invariance Geometry (sig) research program: any complete operational intelligence overa domain with nonzero deterministic admissibility exposure must contain a nonemptydeterministic admissibility function. The internal derivation is stated from a probabilistic–deterministic decomposition of admissibility, AΩ = pΩPΩ ⊕ dΩDΩ, in which the two coefficientsare independent structural exposures rather than complementary probabilities. Theresult is then triangulated through three independent external routes. The cybernetic routeis a single two-stage route: Ashby’s law of requisite variety supplies the capacity condition —effective deterministic-regulatory variety must scale with the operational variety exposedby the probabilistic–semantic side, with an absolute limit at fixed regulator capacity —and the Conant–Ashby good-regulator theorem supplies the representational consequence:effective regulation must embody a model of the relevant regulated distinctions. The formalsupervision and enforcement route combines Ramadge–Wonham supervisory control, thecomplete-mediation principle of protection systems, and proof-carrying code: generableor requested behavior must cross a legal, authority, or proof-validation relation beforeconsequential commitment, whether that restriction is externally visible or compiled into thegenerator. The cognitive-architecture route is supplied by Soar, whose operator proposal,procedural selection, application, and chunking show the same proposal/procedural split,with procedural learning, inside an architecture of integrated cognition. The three routesconverge on a Triangulated D-Inevitability Theorem: complete operational intelligence — inthe system-boundary sense defined in the paper — decomposes as generator ⊕ supervisor.Downstream of the theorem, the D-Relocation Principle states that the established functionis invariant to architectural location — external, internal, or distributed relative to thegenerator. A capacity corollary follows for the present era: general machine-scale semanticgeneration without commensurate growth of deterministic-admissibility capacity raises thelower bound on unresolved operational variety. The triangulated object is the architecturalclass; no claim is made that any particular implementation is the necessary realization.