Joint Lyapunov Certificates for K-Agent Generative AI Governance: Stochastic Stability, Emergent Ensemble Risk, and Zero-Knowledge Governance Attestation

Battle Count: 51

The paper is primarily about AI governance and model risk management rather than trading strategies. However, it has indirect relevance: (1) MRM framework (SR 11-7) is directly applicable to quantitative trading model governance; (2) the coupling gap concept could apply to ensembles of trading models sharing features or fine-tuning data; (3) the noise floor formula provides an audit anchor for model monitoring; (4) the emergent ensemble risk theorem shows how individually sound models can compose fragile systems, relevant to multi-strategy portfolios. The mathematical tools (Lyapunov stability, SDEs, spectral analysis) are transferable to quantitative risk contexts, but the paper does not address trading-specific problems.

High complexity due to multiple advanced mathematical and cryptographic components: (1) Itô SDE analysis with infinitesimal generators and Foster-Lyapunov conditions; (2) Spectral analysis of coupling matrices (eigenvalues, symmetric parts, normal vs non-normal); (3) ZK-SNARK circuit construction (Groth16, Cholesky factorization verification, Poseidon hashing); (4) Euler-Maruyama simulation of coupled multi-agent systems; (5) Governance workflow integration with ledger systems. The theoretical framework requires expertise in stochastic processes, linear algebra, cryptography, and regulatory compliance. However, the core stability check (γ < α_self/|λ_min(A_sym)|) is computationally simple once the topology is known.

All simulations use fixed seeds (seed 42 for initial conditions, seed 77 for Wiener increments), documented Euler-Maruyama discretization (Δt=0.01), and explicit parameter specifications. Study C3 uses configuration-dependent seeds for statistical independence. However, no GitHub repository is provided, and the paper is purely theoretical with synthetic simulations rather than real data. The mathematical proofs are self-contained and verifiable. Five numerical studies (C1-C5) are fully specified with reproducible parameters.