Kappa-FIN: Topological Early Warning System for Financial Market Crises

Kappa-FIN applies the Kappa Method — persistent homology H₁ of rolling correlation networks combined with Forman-Ricci curvature — to detect systemic risk precursors in financial markets. The system uses two complementary criteria (Rayleigh: Ohio Number Oh; Prandtl: damage integral φ) with automated CALM baseline identification (including the KCPT knee-phi-tail anti-contamination penalty) and dual crossing detection. Validated across seven historical crisis scenarios including the 2008 Global Financial Crisis, COVID-19 crash, dot-com bubble, 1987 crash, Volmageddon 2018, Euro/Taper tantrum, and the 2022 Fed rate hike cycle.