Keeping the Index Open: The Recommendation-Side Cost of Shared Search and Recommendation
A shared search-and-recommendation index must score new items from features alone because search has no exploration slot. In a public log covering both surfaces over one catalog, $38.6\%$ of held-out query-search impressions show an item never previously shown or visited. For user-cold engagements, the feature-based tower serves this demand without measurable loss against $99$ sampled negatives ($0.9595$ Recall@20 versus $0.9510$ warm). A lexical baseline reaches similar parity, while a full-catalog check remains statistically undecided. Dual-encoder retrieval therefore keeps the index \emph{open} to new items, unlike an ID-softmax recommender that requires retraining. We price this openness on recommendation against six sequential baselines, each retrained and tuned through five rounds on corrected targets. A float32 timestamp bug had reordered leave-one-out targets for $19.7\%$ of users. On MovieLens-1M, warm accuracy trails the strongest retrained baseline by $5.2\%$ Recall@20 and $11.4\%$ NDCG@20. On MIND, the gap narrows to $0.8$--$3.6\%$ relative to the five strongest baselines, though the model ranks sixth of seven. Under strict zero-leakage cold-start evaluation, the content tower achieves $0.172 \pm 0.006$ Recall@20, $1.4\times$ the strongest retrained dedicated method ($0.124 \pm 0.007$) and $3\times$ a training-free floor, without cold-specific training. Exact full-softmax training raises Recall@20 by $54\%$ on MIND-small and $6.9\%$ on MovieLens-1M over sampled InfoNCE, but recomputes the full catalog each step and exhausts accelerator memory at $240$K items. Approximate nearest-neighbor search explains none of the remaining gap, serving cost does not regress against ID-softmax retrieval, and a history-window sweep explains half the post-recipe remainder. Exact-quality training at catalog scale remains the open problem.