The Geometry of Economic Tension: From the Structural Unified Field to Sustainable Path Optimization

This paper develops a geometric theory of economic existence and sustainability based on the Structural Unified Field (SUF) and its economic-domain projection, the Economic Relativity Model (ERM). Economies are conceptualized as open energy–information systems sustained by non-zero tension gradients (β) and organized through paths that govern dissipation. The SUF principle—existence through tension and optimization through minimal paths—is reformulated for ecological economics. Three nested conditions define system vitality: existence (β ≠ 0), sustainability (net dissipation below renewal capacity), and optimality (minimal path length for a given potential F). From this structure emerge two universal decline mechanisms: administrative distortion, which extends paths and generates reverse potentials, and monopoly closure, which freezes adaptive path renewal. Complexity is redefined as a path function rather than a technological rank; progress occurs only when new layers shorten effective distances. The resulting framework links energy efficiency, market coordination, and institutional design through a single geometric criterion: sustainable welfare improvement requires path shortening and dissipation minimization under fixed β and F. Conceptually, it extends ecological economics from allocation analysis to the geometry of tension and entropy, offering a unified foundation for growth, policy, and resilience across human and natural systems