The Zero-Equity Constraint in Monetary Systems

Version 5.3.0 (August 2026) Introduces Adolf Reinach’s analysis of claim–obligation correlativity as an ontological antecedent for the Monetary Settlement Relation.Version 5.0.0 (July 2026) This release represents a mature version of the paper, following substantial refinement of both the theoretical framework and its presentation. Major changes since Version 4.1.0 include: Settlement relations established as the primitive ontology, with the Settlement Identity introduced as the primary structural result. Economic value as the settlement substrate expanded and promoted to a dedicated section. New Appendix C extending the framework to commercial banking and heterogeneous credit structures. Comprehensive notation audit and standardisation throughout the manuscript. Expanded figures and geometric illustrations, including simplex-based representations. Strengthened historical context, quotations, references, and discussion of the paper's intellectual lineage. Extensive improvements to exposition, organisation, and internal consistency. Abstract Contemporary monetary analysis treats money primarily in operational terms while leaving its underlying ontological status implicit. The present paper develops an explicit ontology of money. 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.