Lean-Verified Handshake: A Mechanized Commitment Kernel Against Coordination Failure Among Opaque AI Agents

Multi-agent AI systems in high-stakes infrastructure face a recurring failure mode: rational opaque agents may defect even when mutual cooperation is Pareto-optimal, typically when defection is risk-dominant. Program-equilibrium theory shows that binding commitment devices restore cooperation, but every existing instantiation either assumes adversarial source-code mutual reading or remains pen-and-paper. Neither approach is operationally accessible to opaque LLM agents. We present Lean-Verified Handshake, a Lean 4 mechanization of a binding-attestation wrapper for cooperative multi-agent AI: routing all agents through the wrapper makes attesting Cooperate weakly dominate attesting Defect over any Stag-Hunt-ordered $2{\times}2$ game (symmetric or asymmetric) and any $n$-player Stag-Hunt-ordered game with all-cooperator and all-defector endpoints, with mutual cooperation as the unique Pareto-undominated Nash equilibrium of the resulting meta-game. The oracle-trust assumption is mechanized as a TrustedOracle typeclass with an explicit truthfulness predicate, instantiated by a worked deterministic-chain oracle and accompanied by a non-instance counterexample witnessing that the obligation is non-trivial; TEE attestation and DIDs/VCs are sketched at the design level. Build-time #print axioms assertions confirm dependence only on Lean 4's standard foundational axiom set (kernel + Classical). We position the resulting verified commitment kernel as a candidate verifier component for the Guaranteed Safe AI agenda, and as a building block for trustworthy multi-agent AI deployed for socially beneficial coordination.