Judgment Operators: A Composition-Invariant Substrate for Multi-Agent Action Spaces

As large language models (LLMs) are increasingly composed into heterogeneous multi-agent systems, a fundamental reliability challenge emerges: knowledge and governance fragment across agents, leading to composition-dependent behaviors and linear scaling of violations. Two empirical observations motivate our approach: internal correction methods (Reflexion, CRITIC, Self-Refine) fail to enforce execution-time constraints deterministically, and filter-based methods (LlamaGuard) sacrifice task utility without repair. We introduce Judgment Operators (JO), a decision-time framework implementing four-way intervention semantics (Allow, Edit, Escalate, Deny) via a portable artifact $J=(\mathcal{C},\mathcal{P})$, enabling minimal repair without modifying agent internals. We establish: (1) composition-invariant enforcement with constant violation probability, motivated by a necessity lower bound showing no decentralized scheme achieves $O(1)$ violation probability; (2) sublinear mistake accumulation via JO-A; and (3) semantic preservation for code transformation. Programmatically verifiable constraints provide the formal foundation; empirically, robustness extends beyond this scope (partial mediation 3--5$\times$ better than theoretical worst-case). JO achieves 0% observed violation rate (vs. 48--68% baselines), 13.5--20.5% zero-shot cross-model transfer where few-shot prompting fails, and provides a portable, auditable, and composable interface for governance and capability injection in multi-agent LLM systems.