THE CURVATURE OF ECONOMIC SPACE: A Trust-Determined Metric and Hyperbolic Fragility

This paper develops a geometric reinterpretation of economic structure by introducing the concept of economic space as a manifold whose metric is determined by trust. It argues that economic systems are not fundamentally linear or merely nonlinear, but curvature-bearing structures. The central claim is that the metric of economic space is shaped by acceptance intensity within financial and institutional networks.

When trust density is high, the system approximates a positively curved (elliptic) regime characterized by compact connectivity and absorptive stability. When trust weakens, the structure shifts toward negative curvature (hyperbolic), where small local disturbances generate disproportionate global effects. Crisis is therefore not gradual deterioration but a threshold-based metric redefinition. The system does not collapse; the regime changes. The space remains, but its geometry transforms.

By integrating network topology, threshold dynamics, and curvature-based reasoning, the paper proposes a structural framework that reinterprets monetary instability, inflation concentration, and regime transitions as geometric phenomena rather than scalar imbalances.