HeckeFraudGuard v3.3: Algebraic Verification of Payment Integrity — 0-Hecke Algebras for PSD3-Era Fraud Detection

Formal verification framework for detecting structural integrity violations in payment processing systems under the European PSD2/PSD3 regulatory regime The framework models the payment lifecycle as elements of the 0-Hecke algebra H₀(Sₙ) and proves a faithful embedding theorem: any payment system satisfying three operational axioms (idempotency, stage independence, handoff consistency) is algebraically a 0-Hecke monoid. Key contributions:- 8 fraud patterns as algebraic violations (including braid exploitation, Coxeter type-B escrow bypass, weighted module for partial captures)- Separation theorem proving H₀(Sₙ) exceeds FSM expressiveness- Extended Matsumoto-Tits theorem for canonical reduction at all ranks- KAE embedding with decidability guarantees- Stochastic validation on 50,000 synthetic transactions- Reference implementation (~2,400 lines Python, zero dependencies) Goal is to Submit to FMICS 2026 (International Conference on Formal Methods for Industrial Critical Systems) Package contents:- Paper (PDF, 15 pages LNCS format)- LaTeX source- LNCS class file- Stochastic validation engine (Python)- Validation results (JSON) ************************************************************************Existing POC in React - Upon request