Mapping the Set-Function Geometry of Evidence Utility in Retrieval-Augmented Generation

Evidence selection depends on the structure of generator utility, the search strategy, and the evaluation target. We introduce Evidence Utility Geometry, an exhaustive subset-intervention audit that measures all three within a fixed evidence interface. Across three multi-hop question-answering datasets, three generator families, and controlled versus support-blind six-passage pools, all 18 dataset–model–construction cells exhibit material non-monotonicity and increasing returns. Negative marginals occur in 27.3–37.9% of tests and positive discrete Hessians in 35.5–42.9%. Exact regret decomposition separates the price of filling a budget from positive same-cardinality search loss, including in an eight-passage extension. A complete generation audit evaluates all 64 subsets for 90 existing questions, two models, and both constructions. Generated F1 also exhibits negative marginals and positive Hessians. Likelihood–F1 rank correlations of 0.55 and 0.49 coexist with different optima: at budget three, exact likelihood selection has F1 regret of 0.184 and 0.175 against the exact F1 optimum, and its paired F1 contrasts with fixed likelihood-greedy span zero. Cardinality-standardized comparisons reveal how weighting subset sizes changes cross-size measurements. EUG connects exhaustive structural measurement to exact selection losses and target alignment, identifying where evidence-selection losses arise.