Stochastic Verification Architectures: ZK-FRS Protocols with Polynomial Blinding, Worst-Case Cryptographic Bounds, and Complete Resolution of the MCA Decoding Limit

This paper establishes rigorous cryptographic soundness bounds and a complete struc-tural resolution for polynomial Interactive Oracle Proofs (IOPs) and Zero-Knowledge Suc-cinct Non-Interactive Arguments of Knowledge (ZK-SNARKs) utilizing Folding Reed-Solomon(FRS) schemes. We present a ZK-FRS protocol integrating algebraic polynomial blindingto guarantee zero-knowledge privacy and sound verification under explicit worst-case cryp-tographic bounds. By replacing heuristic average-case error assumptions with an adversar-ial model, we derive exact lower bounds on query complexity required to achieve 128-bitcryptographic security against malicious provers. Furthermore, we completely resolve thelong-standing open challenge of the Mutual Correlated Agreement (MCA) region—situatedbetween the Johnson radius and code capacity (𝜏 ∈ (1 − √𝜌, 1 − 𝜌))—by transforming proto-col randomness into a formal algebraic variable and proving strict polynomial list-decodingbounds via multivariate interpolation, Jacobian transversality, and Bézout’s Theorem. Acomparative security evaluation against state-of-the-art protocols such as FRI, STIR, andWHIR is provided.