Agent communication remains a foundational problem in multi-agent systems protocols such as FIPA-ACL guarantee semantic richness but are intractable for constrained environments, while lightweight IoT protocols achieve efficiency at the expense of expressiveness. This paper presents μACP, a formal calculus for expressive agent communication under explicit resource bounds. We formalize the Resource-Constrained Agent Communication (RCAC) model, prove that a minimal four-verb basis ¶ING, TELL, ASK, OBSERVE\ is sufficient to encode finite-state FIPA protocols, and establish tight information-theoretic bounds on message complexity. We further show that μACP can implement standard consensus under partial synchrony and crash faults, yielding a constructive coordination framework for edge-native agents. Formal verification in TLA+ (model checking) and Coq (mechanized invariants) establishes safety and boundedness, and supports liveness under modeled assumptions. Large-scale system simulations confirm ACP achieves a median end-to-end message latency of 34 ms (95th percentile 104 ms) at scale, achieving competitive or lower latency than representative agent and IoT protocols under the evaluated workloads. The main contribution is a unified calculus that reconciles semantic expressiveness with provable efficiency, providing a rigorous foundation for the next generation of resource-constrained multi-agent systems.