Admission Before Allocation: Exact Operator-Order Counterfactuals for Multimodal Memory

A stale claim can be rejected by a support verifier and still alter an answer: if rejection occurs after a finite citation slate is packed, the vacancy is not refilled with the eligible evidence that lost the allocation opportunity. ReCAP turns this failure into an exact fixed-snapshot intervention, comparing $S_B(A_{\tau }(C))$ with $A_{\tau }(S_B(C))$ while pairing the candidate sequence, support scores, coverage targets, prompt, random choices, generator, and 2,048-token budget. Across the full ScienceQA, DocVQA, and ChartQA test sets, admission before allocation yields a macro task-score gain of +0.47 [0.18, 0.76] points ($p=0.008$), lowers unsupported-answer rates by 0.79/0.77/0.69 points, and removes 0.34–0.43k median tokens from the pre-pack proposal. In five-turn memories that evolve under each serving policy, lineage-confirmed stale carry-over falls from 8.5 to 5.4% over 167 same-image ScienceQA sessions and from 11.8 to 7.6% over 500 document-disjoint MP-DocVQA sessions. With admission fixed first, the complete typed-assembly package reaches 82.1/77.6/69.3 task score and 7.31/6.58/9.48% answer-level hallucination, outperforming the tested top-100 cross-encoder package by 0.6/0.4/0.4 score points. The evidence identifies eligibility-before-allocation as a consequential serving invariant for citation-constrained multimodal memory.