Preserving Decision-Relevant History: Response-Rank Memory for Write-Before-Query Prediction

Before a query is known, a fixed-size writer must preserve the history distinctions that determine a later response. We formulate this write-before-query interface as compression of a history-indexed response field, and derive its linear response-operator geometry, capacity–allocation decomposition, and late-query timing gap. Query-Rank Memory (QRM) is the corresponding spectral writer with nested prefixes, estimated by weighted reduced-rank regression. Across six native history conditions, QRM lowers response MSE in five, while controlled, exchange, and known-effect tests connect the same response field to storage choices and decisions.