One-Write Associative Sketching for Partition-Invariant Lifelong Cross-Modal Hashing

Lifelong cross-modal hashing updates compact image-text indexes as paired data arrive. Task-boundary updates can nevertheless change the items returned for the same query when an ordered stream is segmented differently, even at similar retrieval accuracy. The challenge is to preserve both the current query head and codes written by earlier heads. We propose (\method), which couples prefix learning with one-write indexing. With frozen features, permanent Dice-derived semantic targets and additive moments recover the full-prefix code-and-relation objective. We prove that its unique ridge solution and shared sample-count clock yield identical query heads, historical codes and rankings across taskifications. Perturbation bounds connect approximate moments to retrieval changes. We evaluate cross-partition top-$k$ agreement using the top-$k$ retrieval reproducibility rate, the mean Jaccard overlap of returned sets, alongside relevance. Across four datasets and three paired seeds, the analytic core returns identical sets and ordered lists at $k=10,20,50$. Clocked discrete extensions retain this agreement, and fixed-gallery query calibration achieves the highest mean average precision on all four datasets, reaching 92.68% on MIRFlickr-25K at 64 bits when averaged over both retrieval directions.