Under a fixed embedding-storage budget, recommenders can use a small full-precision model, a distilled student, or a higher-rank low-precision model. We asked which choice preserves rare-item recall and whether teacher fidelity reflects it in seven dataset-backbone cells: matrix factorization on Gowalla, Last.fm, Amazon Video Games, Steam, Goodbooks-10k and MovieLens-20M, and LightGCN on Amazon Video Games. Seven candidates fit in 168 bytes per user or item row: 40-dimensional Bayesian personalized ranking (BPR), two 40-dimensional unbiased knowledge distillation (UnKD) students, and factorizations of a 300-dimensional teacher's scores at ranks 40, 80, 155 and 300, stored in 32, 16, 8 and 4 bits. Each test set was evaluated once after fixing candidates and confirmatory analyses. The rank-300 4-bit factorization used 13% of teacher storage and retained 95-103% of its tail recall@20 and 93-97% of its NDCG@20 in every cell. The rank-40 factorization had the lowest tail recall in every cell; the 4-bit factorization had 1.2-12.7 times its tail recall and 0.99-1.46 times its NDCG. UnKD students retained 56-102% of teacher tail recall. In all ten prespecified comparisons across five prospective-expansion cells, the 4-bit factorization had higher tail recall, with simultaneous 95% intervals excluding zero. Teacher-hit retention, the share of the teacher's relevant tail hits also found by a model, ordered 23 of 147 candidate pairs differently from tail recall and identified the wrong tail-recall leader in 3 of 7 cells: models can find relevant tail items the teacher misses. In these cells, spending bytes on rank rather than precision preserved rare-item recall at 7.5 times the arithmetic per score. Compressed recommenders should be judged by total tail recall, not teacher fidelity alone.

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