Version 3.0.0 (March 2026) Major revision. This version introduces an explicit treatment of the exclusion of the monetary authority from the set of economic agents and further develops the resulting zero-equity constraint. New sections include “The Benevolent Counterfeiter” and “The Exclusion of the Monetary Authority.” The paper has also been retitled “The Zero-Equity Constraint in Monetary Systems.” General editing and structural improvements have been made throughout. Abstract Monetary theory lacks a clearly articulated ontological account of money. The present paper develops such an account. It proposes that fiat-denominated money—whether issued by the state or by private banks—is best understood as a transferable claim for value: an entitlement to real goods, labour, and services, rather than a commodity-like asset. From this relational interpretation follows a fundamental structural result. Aggregate financial equity is identically zero among economic agents within the monetary system. Every monetary claim resolves to an obligation borne within that same domain. The monetary authority, as issuer of the unit of account, is not itself a member of this set and does not possess financial equity. The value anchor of fiat money is clarified as a dispersed and continuous settlement obligation embedded in ordinary economic activity. Taxation functions as the institutional mechanism through which monetary claims are redeemed in real settlement and retired. On this foundation, monetary financial positions are decomposed into equity (net nominal claim position) and credit (the capacity to issue or expand claims). Credit subsumes equity. This decomposition applies symmetrically to state-issued fiat and bank-created money, providing a unified ontology for contemporary monetary systems. This is a preprint. A revised version may be submitted elsewhere.