Multi-Agent Coordination via Evolutionary Coverage Maintenance: Formal Proof and Benchmark Evidence

We present formal mathematical proofs and empirical benchmark evidence for a novel multi-agent intelligence system that addresses a structural limitation shared by all standard optimization algorithms: when deployed on coordination tasks requiring simultaneous coverage of multiple objectives, selection-based methods converge the population to a single local optimum, leaving the majority of the problem space unresolved; quality-diversity methods address coverage but sacrifice solution quality. Our system resolves this through a runtime-verified framework combining evolutionary dynamics with a novel coordination mechanism. Two theorems are proved and verified at runtime with error below 10⁻⁸. On a coordination benchmark against six established baselines — including the Quality-Diversity state-of-the-art — our system achieves 100% peak coverage with 3.3× superior fitness over the closest competitor (Cohen's d = −9.59, p < 10⁻⁸, 51 runs). Ablation confirms that a single structural component accounts for the entire coordination effect. Results are fully reproducible via a single shell command.