Proof-Carrying No-Arbitrage Surfaces: Constructive PCA–Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates

Battle Count: 68

Directly addresses the core challenge of joint SPX-VIX option surface calibration, which is fundamental to quantitative trading in equity derivatives. The no-arbitrage guarantees, Dupire local volatility stability, and chain-consistency across maturities are essential for delta-hedging, volatility trading, and risk management. The end-to-end risk bound and auditable certificates make it production-ready for trading desks. The c-EMOT bridge with martingale constraints directly enforces the no-arbitrage conditions required for valid option pricing and hedging strategies.

Extremely complex multi-stage pipeline requiring: (1) PCA-Smolyak constructive approximation with anisotropic sparse grids, (2) ReLU compilation with DC decomposition, (3) log-domain tri-marginal Sinkhorn with spectral whitening, epsilon-annealing, and adaptive damping, (4) weighted isotonic regression (PAV) and convex regression for projection, (5) score-based diffusion training with chain-consistency regularization, (6) finite-difference operator stability patches, (7) Gate-V2 decision protocol with alpha-mixing concentration, (8) graph Laplacian spectral analysis, and (9) end-to-end risk bound assembly. Requires expertise in optimal transport, convex analysis, numerical PDEs, machine learning, and financial mathematics. Single 24GB GPU suffices for training but the algorithmic complexity is very high.

The paper provides a comprehensive reproducibility checklist (Appendix A.11) including: data preparation scripts, strike/maturity grids, exact seeds and calendars, configuration files for all runs, a single entry script to reproduce all tables and figures, README with hardware footprint/training time/licenses, and precomputed Blind-Test predictions. All certificates are exported to summary.json and mirrored as LaTeX macros. The Gate-V2 protocol is fully auditable with exported tolerance constants, FIR coefficients, tail fractions, and window sizes.