The Semantic Obligations of Strong Universal Claims: An Evoluist Theorem of Audit-Domain Completeness

This consolidated technical publication is the fourth study in the formal Evoluist research programme. It continues the status-diagonal analysis developed in The Evoluist Theorem: Formal Core, the investigation of distributed and indexed coordination developed in Indexed Evaluative Architectures and Terminal Coordination, and the conditional global framework developed in The Strong Evoluist Structural Alternative. The article develops a formal theory of the semantic obligations generated by regimented strong universal-sufficiency claims. It distinguishes independently defined semantic and procedural domains, represents obligations by typed ten-field records, and introduces provenance-preserving equivalence, collective family coverage, semantic genesis constructors J0–J11, and a certificate-bearing generator G0–G11 operating through finite proof DAGs, finitely generated trace schemas, and simultaneous strongly connected components. Its central result, the Claim-Generated Obligation Soundness and Completeness Theorem (T-IV4 / FTT3-A), shows that for Tier A_spa finite-clause claims and Tier B_eff+spa schema-generated claims satisfying AE1–AE12, the procedural audit domain contains every genuine claim-generated obligation class and no non-obligations. Equivalently, under the stated audit-eligibility and semantic-provenance conditions, AuditDom_U equals ClaimDom_U and SoundComplete_U holds. The paper does not claim that unrestricted FGSDA and RSUC assumptions alone entail obligation completeness. Effective instance access, independently adequate semantic provenance, exact canonical-token generation, five-checkpoint audit completeness, and proof-assistant mechanisation remain separate or open theorem targets. The publication includes the Main Article and an accompanying Technical Supplement containing the complete typed definitions, quotient foundations, G0–G11 and J0–J11 specifications, certificate-validity and soundness proofs, semantic-genesis and global-recovery proofs, adversarial countermodels, dependency tables, result registries, and the mechanisation blueprint.