The Axiom of Happiness: A Mathematical Framework for Sustainable Well-being as Structural Circulation in Finite-Resource Systems

v1.0: First release. Mathematical formalization of the Axiom of Happiness white paper (DOI: 10.5281/zenodo.17461137). Embeds the EARM well-being cycle (Engagement, Accomplishment, Relationships, Meaning) into the Unified Constraint Dynamics framework, with Positive Emotion P(x;kappa) as a context-dependent cost-sensor. Proves that fixed P values lead to terminal circulation collapse (Proposition 1) and that sign-reversal of the third central moment enables a candidate optimal circulation point (Proposition 2). Acceptance is modelled as the operational principle enabling context-sensitive redistribution of value. The three-collapse structure (S/B/D) and beta=1 scaling are imported as Scaling Ansatze from UCD. Six falsifiable predictions are stated. v2.0 (April 2026): Added explicit connection to the narrative-psychological tradition. Introduction now situates the Dual Reality Structure within the lineage initiated by Sarbin (1986) and Bruner (1991); Section 4 includes a new Remark on narrative psychology citing Sarbin, Bruner, and Crossley (2000). No changes to propositions, predictions, or mathematical content. v3.0 (April 2026): Added Remark on the Maxwell-type dual role of Positive Emotion P as the structural origin of its fuel-sensor duality. The formal isomorphism with Maxwell's electromagnetism is imported as a Scaling Ansatz; establishing a rigorous correspondence between the EARM Gibbs family and Maxwell-type field structures is left as an open problem. No changes to propositions, predictions, or mathematical content.