LLM-based query expansion improves retrieval by generating document-like passages. In hybrid retrieval, however, most evaluations fuse fixed top-$L$ dense and sparse rankings. Because the cutoff controls both which cross-channel contributions enter fusion and how much of each ranking is accessed, gains measured at one $L$ can change or reverse at another. We separate these effects by evaluating retrieval effectiveness under complete-list fusion and recording the policy-specific per-channel replay stopping depths at which its ordered top-$K$ is certified. We then introduce DESA (Dense Expansion and Sparse Anchoring), a channel-asymmetric query expansion method. An LLM generates complementary reference passages; orthogonal residual expansion adds their new semantic directions to the dense query, while score-product anchoring incorporates their lexical cues into sparse retrieval without broadening the original query's lexical support. Across seven BEIR datasets, DESA improves nDCG@10 and Recall@20 over the unexpanded query by 3.82% and 2.38%, while reducing dense and sparse access depths by 36.90% and 36.56%. With equal dataset weighting, 63.31% of queries become shallower in both channels. However, both depths increase with Contriever on Touch\'e-2020. These results support channel-specific integration of generated passages and joint evaluation of retrieval effectiveness and access depth.
Modern retrieval-augmented generation (RAG) systems often fuse fixed Top-$L$ results from dense and sparse retrievers, treating later contributions as zero. The cutoff therefore determines both the ranking and its execution cost. Yet truncated fusion is not generally equivalent to complete-list fusion: unread cross-list ranks can change Top-$K$ membership or order even when the observed candidates contain every item in the complete-list Top-$K$. Because channel rankings vary across queries and corpus updates, a depth selected from historical queries may not transfer reliably. We propose Exact Adaptive Hybrid Retrieval (EAHR), which fixes the ordered Top-$K$ defined by complete-list weighted RRF as the retrieval target and treats channel depth as request-specific execution state. Per-Vector Scalar Quantization (PVS) and Posting Block-Max (PBM) produce resumable exact dense and sparse rankings. Fusion bounds unread contributions and requests further ranks only while they can change the Top-$K$. Every successful request therefore matches complete-list fusion without a preset Top-$L$; otherwise, execution continues safely to list exhaustion. Across five test collections and five temporal corpus snapshots, complete-list weighted RRF remained competitive, whereas fixed depths selected from historical queries did not transfer reliably. EAHR reproduced the complete-list ordered Top-20 in all 150 query-snapshot combinations. Under a warm-cache, interleaved, order-balanced protocol, the paired geometric-mean latency ratios of exhaustive batch execution to EAHR were 23.35 on TREC-DL 2019 and 30.28 on TREC-DL 2020. Anti-correlated rankings exhausted both lists, and some difficult queries were slower with EAHR. EAHR does not guarantee a speedup for every request; it fixes the exact result while adapting execution depth to the current rankings.
