Computational Jurisprudence: Verifiable Law for Machine Societies

Autonomous AI agents now hold funds, delegate authority to other agents, and transact at machine speed; the governance apparatus meant to constrain them—policies, audits, compliance—remains documentation-based and human-latency. This mismatch cannot be closed by better monitoring or filtering: compliance must become a runtime, compositional, proof-carrying property of computation itself. We call the resulting discipline computational jurisprudence. This article surveys the four literatures the discipline must synthesize: object-capability security; verifiable, proof-carrying, and zero-knowledge computation; policy-as-code and computational law; and agentic AI with its emerging payment protocols. Each supplies a mature mechanism the others lack; none supplies a complete normative substrate. The synthesis is organized in three pillars: (i) a delegation calculus under which authority can only attenuate as it propagates between agents; (ii) runtime compliance proofs, a three-tier evidence regime (attested, optimistic, and zero-knowledge); and (iii) sealed delegation chains with graduated attribution, which reconcile the privacy of capability-based authority with the accountability that adjudication requires. A case study on agentic payment protocols grounds the architecture and reports first measurements: capability verification versus a centralized policy decision point, end-to-end enforcement on the x402 payment path, and accumulator-based revocation. Seven open problems define the research agenda.