Obligation Finality, Custody-State Integrity, and Consequential Financial Closure

This paper develops a formal architecture for obligation finality, custody-state integrity, and consequential financial closure in financially consequential systems. The architecture treats terminal financial state as a governed classification problem rather than as a simple endpoint observation. It separates obligation state, custody state, finality state, and consequential-closure state, and preserves the distinction between what occurred, what was authorized, what obligations remain, who validly controls or holds the relevant object, what may be declared final, whether a completed state may later reopen, and what historical evidence must survive that reopening. The central architectural boundary is: Finality ≠ consequential closure. The paper further preserves the following non-collapse relations: execution does not establish finality; consensus does not establish finality; atomic completion does not establish finality; reconciliation does not establish finality; custody possession does not establish custody authority; custody possession does not establish finality; finality does not establish irreversibility; finality does not establish continuity preservation; and consequential closure does not imply impossibility of reopening. F3 inherits the post-effect financial-state semantics established in Partial Settlement, Compensating Execution, and Economic-State Continuity and the distributed-settlement architecture established in Distributed Settlement, Multiparty Authority, and Economic-State Continuity. The controlled F3 proof corpus closes forty proof obligations under three distinct evidence classes: twelve FORMALLY-PROVED obligations, twenty-two COUNTEREXAMPLE-DISCHARGED obligations, and six REFERENCE-RUNTIME-CONFORMANT obligations. The publication also records fourteen adversarial verification cases. These evidence classes remain intentionally non-interchangeable. This publication is part of the ORYNTH Financial Systems Series and establishes the series' terminal-state substrate for obligation finality, custody validity, reopening, historical preservation, and consequential financial closure.