Version 4.1.0 (May 2026) This revision generalizes the credit representation into a family of admissible transformations yielding zero-sum credit representations. Appendix B introduces the resulting gauge family and clarifies the distinction between coordinate representation and underlying economic invariants. Version 4.0.0 (April 2026) This revision introduces a transformation showing that a fiat monetary system admits a credit representation. The construction removes the monetary authority as an economic agent and establishes the zero-equity constraint structurally. Appendix A provides a self-contained mathematical formulation of this result. 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, services, and the use of natural resources, 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 carries no obligation in real economic settlement, and may properly be excluded from this set. 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). This decomposition applies symmetrically to state-issued fiat and bank-created money, providing a unified ontology for contemporary monetary systems. The exclusion of the monetary authority from the set of economic agents is established mathematically through a family of admissible transformations yielding zero-sum credit representations. This is a preprint. A revised version may be submitted elsewhere.
Patrick McGuinness (Fri,) studied this question.