PQ-EID: Provenance-Quotient Evidential Interaction Decomposition and Certification in Web Question Answering

Web question answering often relies on passages that repeat the same source, offer independent support, or affect an answer only when considered together. We present PQ-EID, a method for examining how evidence interacts while accounting for its provenance. The method groups passages by claim and source information, evaluates evidence coalitions, and uses Möbius decomposition to identify individual and joint contributions. It also assesses whether an interaction keeps the same sign across plausible provenance groupings, subject to explicit bounds on evaluation error. Controlled experiments recovered known interactions and showed how mistaken source grouping can change their interpretation. A 10-question Question Answering with Conflicting Contexts (QACC) pilot revealed sensitivity to duplicated passages, although raw-context counting gave better predictive scores. We also evaluated two instruction-tuned language models on 60 QACC questions. Their coalition scores showed substantial higher-order interactions and sensitivity to the order of evidence. A separate controlled study of 80,000 trials examined when the conditional sign certificate succeeds and how it can fail if the true provenance structure is excluded. In the simulation with uncalibrated partition weights, 3.3–9.6% of the issued signs were wrong in the regimes where signs were issued. The real-data experiments use domain- and claim-based source proxies, without verified derivation chains. PQ-EID is therefore presented as a method for auditing evidence structure; its statistical guarantees apply under the stated structural and evaluation assumptions.