The Axiomatic Foundation of the XY Fiscal Framework

The Axiomatic Foundation of the XY Fiscal Framework Two Capitals, Two Directions, One Reclassification Mechanism, and the Going-Concern Condition Author: Jim Y. Huang *1 Year: 2025 Abstract This technical note provides the minimal axiomatic basis of the XY fiscal framework. The framework identifies two fundamental substances—tax-financed public capital and post-tax private capital—and two irreducible directions of motion: cross-jurisdictional horizontal shifts (X) and downward intergenerational transmission (Y). Institutional events function as fiscal reclassification processes that relocate resources between before-tax and after-tax positions and between public and private forms. By extending the going-concern assumption from accounting to entire societies, the note treats continuous flows along both axes as the precondition of social continuity. While public and private capital are familiar categories in public finance, they have rarely been formalized as the atomic units of a social geometry or linked to accounting’s structural logic. The XY framework unifies these strands into a closed, self-consistent geometric description of institutional life. Keywords: XY fiscal framework, axioms, public capital, private capital, going concern, reclassification, intergenerational descent, cross-border movement 1. Axiom 1 — Two Types of Capital (Substance Axioms) All resources relevant to institutional life appear in one of two fiscal forms: 1. Tax-financed public capital Generated collectively through taxation, it circulates through education, health, infrastructure, legality, and other public systems. It enables and sustains horizontal movement across jurisdictions. * PhD Student, University of Toronto (OISE). LL.M (Tax Law), Osgoode Hall Law School. Chartered Professional Accountant (CPA, Canada); Cer�fied Prac�sing Accountant (CPA, Australia); Trust and Estate Prac��oner (TEP). Research focuses on fiscal architecture, cross-border capital movement, intergenera�onal posttax capacity, and ins�tu�onal inequality. 2. Post-tax private capital Held by individuals and households, it includes assets, skills, savings, debt positions, and accumulated human capital. It descends vertically across generations through inheritance, care, and investment. These two forms are exhaustive: there is no third type. Every resource is either public or private at any given fiscal moment. 2. Axiom 2 — Two Directions of Movement (Directional Axioms) Capital moves through only two independent directions: 1. Horizontal movement (X) Occurs while individuals are alive. It traces cross-border and cross-regional mobility through rule-defined environments—jurisdictions, markets, districts, institutions. 2. Vertical movement (Y) Occurs after horizontal life ends. Post-tax private capacity flows downward only across generations. It never flows upward. These two directions are exhaustive: There is no third independent axis of movement. 3. Axiom 3 — One Institutional Mechanism (Reclassification Axiom) Institutional events act by reclassifying the fiscal position of resources. Reclassification includes: • before-tax → after-tax • after-tax → before-tax • private → public • public → private • jurisdiction A → jurisdiction B Every institutional interface—taxation, benefit rules, school boundaries, residency criteria, inheritance law, incorporation law, student loan rules, migration policy—is a reclassification mechanism. Thus institutional life is a sequence of fiscal transformations, not merely narratives. 4. Axiom 4 — The Going-Concern Condition (Continuity Axiom) Accounting treats a firm as a going concern if it is expected to continue operating. A society can be interpreted the same way: it is a going-concern entity composed of firms, households, and public bodies whose survival depends on continuous capital circulation. • A firm survives through cash flow. • A society survives through fiscal flow. Under the going-concern condition: • public capital must continue flowing horizontally (X) • private capital must continue descending vertically (Y) Without flows along both axes, the society’s continuity fails. Going concern therefore requires the XY geometry. 5. Derived Result — The XY Fiscal Plane as the Minimal Social Geometry From Axioms 1–4, it follows that: • two capitals (public/private) = the substances • two directions (X/Y) = the paths • one mechanism (reclassification) = the action • going concern = the continuity condition Together, these axioms generate a closed, minimal, and self-consistent coordinate system. The XY fiscal plane is not a modeling choice. It is the necessary geometry implied by the conditions under which a society can exist, reproduce, and classify resources over time. 6. Corollary — Micro Trajectories to Macro Descent Individual life-paths trace horizontal trajectories on X. Family-level transmissions trace vertical descent on Y. When many such paths are superimposed, they produce the collective structure of a society’s intergenerational distribution of post-tax capacity. Thus: • X records how individuals move through space. • Y records how society extends itself over time. Micro behaviors project into macro structures through the XY plane. Suggested Citation Huang, J. Y. (2025). The Axiomatic Foundation of the XY Fiscal Framework: Two Capitals, Two Directions, One Reclassification Mechanism, and the Going-Concern Condition. Zenodo Technical Note.