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. We introduce **Judgment Operators (JO)**, a decision-time framework that adapts corrective projection via precedent memory from agent actions onto admissible sets. JO establishes a *unified projection interface* in which governance constraints $\mathcal{C}$ define the *target admissible set* and corrective precedents $\mathcal{P}$ provide *executable corrective knowledge* for adapting the projection map. The centralized operator $\Pi_J: \mathcal{X} \to \mathcal{X}_J$ implements four-way intervention semantics (*Allow*, *Edit*, *Escalate*, *Deny*), enabling minimal repair without modifying agent internals. We formalize JO as an *adaptive projection operator* and establish guarantees of: (1) **composition-invariant enforcement** with **constant violation probability** (vs. linear scaling without JO); (2) **sublinear mistake accumulation** for online adaptation via JO-A under recurring violations; and (3) **semantic preservation** for code transformation tasks via structure-preserving projection. Empirically, JO provides *portable corrective knowledge transfer*: (1) **capability**---learns and reuses corrective precedents under recurring violations, improving task success over strong baselines; (2) **governance**---achieves *near-perfect constraint enforcement* in fully verifiable settings (0\% observed violation rate vs. 48--68\% for baseline methods); and (3) **portability**---enables *13.5--20.5\% absolute zero-shot cross-model transfer* where few-shot prompting fails. Judgment Operators thus provide a **portable, auditable, and composable interface** for both decision-time governance and capability injection in multi-agent LLM systems, addressing fragmentation at its architectural root through **adaptive, composition-invariant projection**.