Ghosts Without Target Shift : Exact Admissibility for Stochastic Candidate Reuse

Language-model evaluation often assigns an expensive judgment only to the response selected from a stochastic candidate batch. Unselected responses can supply control information, but proxy alignment or variance reduction alone does not establish that reuse preserves the selected-response target, respects an externally certified score envelope, and repays its full cost. We introduce Target-Preserving Ghost Qualification (TPGQ), which combines a policy-centered correction, Support Projection, and qualification on independent calibration data. Preselection centering preserves the target, and projection enforces support; independently supplied conditional slot means give variance optimality within the certified feasible class. We derive exact range-sensitive and componentwise cost boundaries under registered planning and ledger assumptions. In a controlled clustered instance, projection lowers variance by $2.857\%$ and the continuous planning cap by $2.521\%$ relative to feasible Global Coefficient Shrinkage. An independent-split study obtains an admissible projection-active decision and a disjoint variance ratio of $.6224$. A 2,304-cell audit identifies constraints missed by simpler rules; two sealed reward-model reconstructions explain headroom rejection. The results establish controlled feasibility and interpretable real-pipeline boundaries.