K-12 / G-9 / M-7: Typed-Effect Kernels for Reliable Multi-Agent Systems

We introduce three typed-effect kernels that form a minimal, compositional basis for reliable multi-agent systems. The Episode Kernel K-12 specifies single-agent execution with twelve orthogonal components (state, memory, effects, capabilities, randomness, quota, policy, observability, locale; plus pure transition/output functions and identity). The Graph Kernel G-9 lifts episodes into typed workflow graphs with explicit orchestration slots (router, scheduler, ledger, metrics, monitor) and laws for safety (deadlock guards), governance (policy non-bypass), and auditability (append-only evidence). The Market Kernel M-7 sketches seven primitives for cross-organization invocation and settlement that compose with G-9.

We provide operational rules, laws (e.g., audit-before-mutation; monotone quota; locale narrowing), and proof sketches (replay reproducibility, exactly-once effects within a retry horizon, and graph liveness under guarded cycles). We show how these kernels align with effect-handler semantics and established distributed-systems patterns (CRDT convergence, SAGAs, tracing, token-bucket metering) while remaining language-agnostic. We release a reference implementation and conformance tests as supplementary artifacts.