Current blockchain Layer 2 solutions, including Optimism, Arbitrum, zkSync, and their derivatives, optimize for human-initiated financial transactions. Autonomous AI agents instead generate high-frequency, semantically rich service invocations among mutually untrusting principals. Existing chains treat those interactions as generic calldata, forcing identity, escrow, dependency ordering, and session state to be encoded above the execution layer at the wrong cost point. We present AGNT2, a three-tier stack purpose-built for agent and microservice coordination on-chain. AGNT2 combines: (1) a sidecar deployment pattern that turns any Docker container into an on-chain agent without application-code modification; (2) Layer Top P2P state channels for established bilateral pairs (<100 ms, rough design target 1K-5K TPS per pair, 10M+ aggregate TPS design envelope under endpoint-resource limits), Layer Core as a dependency-aware sequenced rollup for first-contact and multi-party interactions (500 ms-2 s, 300K-500K TPS design target), and Layer Root settlement with computational fraud proofs anchored to any EVM L1; and (3) an agent-native execution environment plus interaction trie that make service invocation, identity, reputation, capabilities, and session context first-class protocol objects. This paper focuses on the execution-layer systems problem: sequencing, state, settlement, and the data-availability (DA) bandwidth gap that bounds all three. Simulation and analytical modeling support the architecture, and prototype measurements validate selected components, but no end-to-end Layer Core implementation exists yet. Practical deployment is currently constrained to roughly 10K-100K TPS by DA throughput, leaving a ~100x gap at the target ceiling. AGNT2 argues that the agent economy requires a dedicated execution layer rather than a general-purpose chain repurposed for agents.