Basin Instrumentation and Thin–Margin Theory

Basin Instrumentation and Thin–Margin Theory develops the methods required to detect, localize, and manage instability in near-critical systems where global metrics fail. The paper shows that stability is inherently basin-localized and that thin margins render systems hypersensitive to curvature, mixed-gate interactions, and observer effects. It introduces basin-restricted spectral instrumentation, occupancy observables, and early-warning indicators that detect instability before global failure. The theory provides a precise geometric account of why near-critical systems appear stable while harboring imminent collapse within specific basins.