Synthesis: Recursive audit closure across domains

Six notes have isolated the conditions, capacity relation, use channel, design partition, dynamics, and domain instances of one evaluation failure. This note states the joint object. Recursive audit closure has four elements: a categorical benchmark, institutional reliance on its judgments, a channel from judgment to the next population, and an auditor whose verification capacity is bounded by shared substrate. Closure makes measurement part of the production function. It does not by itself determine the direction of change. Erosion requires a second triad: proxy misalignment, differential learnability, and a verification deficit that lets the rewarded proxy outrun task-relevant evidence. Lineage independence, an uninhabitable anchor, and rate parity block exposures at different points; they are not a row-wise translation of the erosion triad. The distinction preserves the perfect-alignment counterexample: recursive selection can improve a task when the rewarded signal remains faithful to it. Instances from structured finance, AI evaluation, citation indexing, standardized testing, and peer review are aligned against the two layers. Their common loop organizes the comparison; their different anchors and evidence depths explain why the available exits and warranted claims differ. The resulting proposition is dynamical: once measurement feeds what it measures, its validity belongs to the trajectory of the loop rather than to the instrument in isolation. The framework closes with four tests — combination, channel measurement, resistant-domain survey, and empirical execution — on which the synthesis can lose.