Financial institutions are beginning to deploy agentic workflows in credit, fraud, collections, compliance, and operational control. Governance remains largely component-centric: each model or agent is specified, tested, authorized, and monitored locally. That is insufficient when institutional risk arises from the joint behavior of many locally acceptable components. We call this gap constitutional non-compositionality: local compliance checks need not compose into acceptable collective outcomes such as bounded disparate impact, market integrity, or traceable accountability. We propose ARIA as a finance-specific reference architecture and falsifiable research agenda for agent-population governance. It organizes six capabilities across normative-accountability, execution-control, and assurance-learning planes: policy specification, population-level observed-versus-expected behavior monitoring (M2), bounded authority, runtime containment, adaptive policy change, and preserved human oversight competence. Two simulations illustrate shared-signal thin-file exclusion under local controls and earlier warning from observed-versus-expected distributional monitoring in a constructed drift regime. The contribution maps these controls to fair-lending, EU AI Act, model-risk, and conduct-supervision evidence needs, and closes with a validation agenda rather than a production-effectiveness claim.

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