The Structural Audit of Strong Universal Claims: An Evoluist Theorem of Five-Checkpoint Completeness

This publication is the fifth study in the formal Evoluist research programme. It continues the status-diagonal analysis developed in The Evoluist Theorem: Formal Core(I), the distributed and indexed coordination framework developed in Indexed Evaluative Architectures and Terminal Coordination(II), the conditional global architecture developed in The Strong Evoluist Structural Alternative(III), and the audit-domain completeness result established in The Semantic Obligations of Strong Universal Claims: An Evoluist Theorem of Audit-Domain Completeness(IV). The article develops a formal theory of structural audit for the complete provenance-sensitive obligation domain inherited from the preceding study. It introduces five ordered checkpoints — Scope/Closure, Internality, Frame/Rank/Context, Terminal Settlement, and Exact Operative Determinacy — together with typed positive pass and failure witnesses, token/family/SCC/finite active generative-instance audit objects, and a residual-open normaliser N5∗. Its central result, FTT3-B, proves that for the applicable Article IV theorem tiers under independently stated factorisation-admissibility conditions, the inherited obligation domain is five-checkpoint audit-complete: every obligation class admits a licensed five-normal audit presentation, semantic non-realisation yields a qualified first failure, and every licensed first failure lifts to one of the exact positive structural limitations L1–L5 of Article III. A strengthened residual theorem (T-V5+) independently represents semantic in-class obstructions, partitions them through the R6-01–R6-16 adversarial families, and establishes universally quantified safe reductions to one of the five independently defined failure families. Cor-V1+ therefore excludes a genuine semantic sixth failure in the exact typed, provenance-controlled, finite or finite-instance, factor-admissible scope. The article additionally establishes qualified first-failure stability, structural witness lifting, provenance-sensitive concordance with the Article III audit interface, and token-level audit transport. The paper does not claim unrestricted fivefold exhaustiveness for arbitrary theories, source-free infinite provenance, or globally completed infinite generative aggregates. It also preserves a strict distinction between provenance-quotient completeness and literal token generation. Literal Article III D120/D124 completeness and direct composition with the original T5 antecedent therefore remain conditional. The final inter-article handoff is established at the provenance-quotient level through Cor-V2-Q. The Zenodo record contains the Main Article and the accompanying Technical Supplement. The Supplement provides the complete D-V1–D-V30 formal interface, witness and checker contracts, the N5∗ normaliser, the theorem chain T-V0–T-V9, the R6-01–R6-16 adversarial programme, residual representation completeness and universal reduction results, transport proofs, dependency audits, and final result registries.