Distributed Settlement, Multiparty Authority, and Economic-State Continuity

This paper presents a system-independent formal architecture for distributed financial settlement that preserves the distinctions among agreement, consensus, authority, admissibility, execution, economic effect, atomic completion, settlement finality, reconciliation, and economic-state continuity. The architecture extends the post-effect financial-state semantics established in Partial Settlement, Compensating Execution, and Economic-State Continuity without redefining them. Distributed partial effect maps into the inherited F1 PARTIAL classification, while compensation and reversal remain independently authorized consequential executions and reconciliation remains distinct from state mutation. The central architectural boundary is: agreement ≠ consensus ≠ authority ≠ admissibility ≠ execution ≠ effect occurrence ≠ atomic completion ≠ settlement finality ≠ reconciliation ≠ continuity preservation The paper formalizes multiparty authority requirements, distributed admissibility, execution-leg composition, atomicity, distributed partial settlement, domain-relative and cross-domain finality, conflict, divergent histories, reconciliation, and continuity preservation. Its controlled evidence surface includes six PROVED results, thirteen COUNTEREXAMPLE-DISCHARGED results, eight reference-runtime-conformance surfaces, twenty-seven adversarial cases, and zero recorded adversarial failures. Formal proof, counterexample discharge, runtime conformance, and external validation remain distinct evidence classes. This publication is part of the ORYNTH Financial Systems Series. It inherits the post-effect financial-state substrate established in F1 and provides the distributed-settlement architecture inherited by downstream obligation-finality and consequential-closure work.