An agent can retain information before receiving a future question and later retrieve evidence from an archive. Evaluating this arrangement requires accounting for both retained information and the width of each retrieval response. Decision-tree capacity bounds describe individual sets of distinguishable records, but a memory writer must encode every possible record before the query is known. We study fixed-length retention beside an immutable binary archive, with a worst-case limit on raw bit or word reads. We characterize feasible one-bit-read memory cells and construct encoders that partition the complete record space. Supporting pairwise exclusive disjunction and conjunction with one bit read is equivalent to supporting every Boolean query. For multiple reads, we combine explicit encoders with decision-tree counting and an entropy converse. The word-read bounds differ by at most two retained bits when the read budget is at most half the archive length. Under an explicit condition on word width and archive length, raw-word caching attains the exact optimum among all writers. A related condition preserves this optimum under positive average error. Exhaustive checks validate the implementations. In a matched dialogue-agent study, a categorical sufficient statistic preserves source decisions with less storage and lower decoding latency than the universal encoder. A catalogue-specific index reduces private state further and requires additional shared storage. The results characterize how response width and future query structure determine retention requirements.

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