When Causal Structure Replaces Replication: Reference-Free Federated Causal Auditing

In federated causal analysis, different data holders may answer different fixed conditional-independence (CI) questions without a common reference answer, so the same reports can support different explanations of the true CI answers and source alignments. We ask when relationships among CI statements can resolve this ambiguity without additional cross-source answers and when such answers remain necessary. For any specified set of possible CI answer patterns, we exactly characterize the surviving ambiguities, when relative source alignment is identified, and, under any fixed set of allowed cross-source requests, the minimum number of additional answers needed, including when identification is impossible. Holding the queries, sources, reporting graph, reporting mechanism, and allowed requests fixed, we prove that a particular four-variable pattern of CI changes and its complement cannot be the exact difference between two DAG-consistent causal explanations, even inside a larger DAG, while the same change is realizable by regular Gaussians. Repeating the construction across disjoint four-variable blocks gives a linear separation with only a linear number of fixed CI questions: DAG structure needs no additional cross-source answers, whereas regular Gaussians need exactly one per complete block, even when every missing source–query answer may be requested. Controlled exact comparisons over the complete ambient-DAG quartet family show that the replication advantage is common across broader reporting patterns, while a separate repeated-task analysis shows an analogous identification benefit under asymmetric stochastic source errors.