Verified Nelson-Siegel COS Hybrid Pricing Framework

We present a formally verified framework for pricing interest rate derivatives using a hybrid approach that combines Nelson-Siegel yield curve dynamics with COS method characteristic function pricing. The framework encompasses 45 machine-verified theorems covering put-call parity relations, positivity bounds for cap and floor prices, SABR volatility constraints, and Nelson-Siegel factor structure properties. Key results include verified cap-floor parity relationships, discount factor contraction bounds, and Arbitrage-Free Nelson-Siegel (AFNS) drift restrictions. The proofs are mechanically verified using the Platonic proof kernel with Z3-backed nonlinear arithmetic, providing a rigorous foundation for production-grade derivatives pricing systems.