Multi-hop question answering requires combining information from multiple documents to answer complex questions. These systems have grown increasingly capable, yet when they fail, the error is typically attributed to not finding the right documents. Whether this holds at the level of individual reasoning steps remains largely unexamined. We investigate this across three standard multi-hop QA benchmarks and find that failures decompose into two distinct modes: retrieval failures, where the needed passage was not retrieved, and extraction failures, where the passage was retrieved but the needed fact could not be extracted — a phenomenon we term the fact-grounding gap. Extraction failures account for nearly half of all per-hop deficiencies and are invisible to standard retrieval metrics. They remain unresolved by every retrieval intervention we test, establishing a ceiling for retrieval-only improvements. The gap’s severity varies across benchmarks and question types, but extraction failures appear on every dataset we measure. Our findings reveal that retrieval failures and extraction failures are fundamentally different bottlenecks requiring different solutions — a distinction absent from current evaluation practice.

Exact nearest neighbor search is a computationally intensive process, and even its simpler sibling — vector retrieval — can be computationally complex. This is exacerbated when retrieving vectors which have high-dimension d relative to the number of vectors, N, in the database. Exact nearest neighbor retrieval has been generally acknowledged to be a O(Nd) problem with no sub-linear solutions. Attention has instead shifted towards Approximate Nearest-Neighbor (ANN) retrieval techniques, many of which have sub-linear or even logarithmic time complexities. However, if our intuition from binary search problems (e.g. d=1 vector retrieval) carries, there ought to be a way to retrieve an organized representation of vectors without brute-forcing our way to a solution. For low dimension (e.g. d=2 or d=3 cases), kd-trees provide a O(dlog N) algorithm for retrieval. Unfortunately the algorithm deteriorates rapidly to a O(dN) solution at high dimensions (e.g. k=128), in practice. We propose a novel algorithm for logarithmic Fast Exact Retrieval for Nearest-neighbor lookup (FERN), inspired by kd-trees. The algorithm achieves O(dlog N) look-up with 100% recall on 10 million d=128 uniformly randomly generated vectors.