The Strong Evoluist Structural Alternative

Abstract

This consolidated technical publication is the third study in the formal Evoluist research programme. It continues the status-diagonal analysis developed in The Evoluist Theorem: Formal Core and the investigation of distributed and indexed coordination developed in Indexed Evaluative Architectures and Terminal Coordination. The article presents a unified many-sorted framework for finitely or generatively specified discriminative architectures that claim unrestricted constitutive scope and determinate application. Its pure formal result, the Lean Carrier Collapse Theorem (T4), shows that Closed Reflexive Naming Adequacy, Local Application Representation, Local Self-Name Precomposition Closure, a faithfully realised fixed-point-free status transformation, and lean same-context status determinacy cannot coexist. The stronger global result (T5) is an audit-relative conditional adequacy theorem. Relative to the explicit provisional five-checkpoint condition AuditComplete⁵, a regimented strong universal-sufficiency claim either activates the local collapse configuration or preserves at least one of five positive structural boundaries: scope or closure, semantic externality, rank or context, non-terminal settlement, or a limitation of exact operative determinacy. The paper does not claim that fivefold exhaustiveness has already been proved for every possible theory or architecture. General representation, regimentation, and five-checkpoint factorisation remain open theorem targets. The publication includes the full formal signature, proofs, countermodels, boundary architectures, dependency tables, and result registries.