Computational Jurisprudence: Verifiable Law for Machine Societies

Autonomous AI agents now hold funds, delegate authority to other agents, and transact at machine speed, while the governance apparatus meant to constrain them (policies, audits, compliance) remains documentation-based and limited by human latency. Better monitoring or filtering cannot close this mismatch: compliance must become a runtime, compositional, proof-carrying property of computation itself. We call the resulting discipline computational jurisprudence. This article is an integrative review of the four literatures the discipline must synthesize, namely, 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, and none supplies a complete normative substrate. The synthesis is organized into three pillars: (i) a delegation calculus, under which authority can only attenuate as it propagates between agents, for which we prove monotone attenuation in the conjunctive caveat fragment and exhibit a counterexample outside it; (ii) runtime compliance proofs, a three-tier evidence regime (attested, optimistic, and zero-knowledge); and (iii) sealed delegation chains with graduated attribution, reconciling capability-based privacy with the accountability adjudication requires. A case study on agentic payments grounds the architecture and evaluates three components on two platforms, with five independent executions each: local capability verification against a centralized policy decision point, enforcement on the x402 payment path, and accumulator-based revocation. What the article offers is therefore a survey, a conceptual architecture with a formal core, and a partial evaluation of three components, not a fully implemented system; a status table marks that boundary component by component. Eight open problems define the research agenda.