Abstract
In any domain where knowledge accumulates under formal authority -- law, drug regulation, software security -- a later document can formally void an earlier one while remaining semantically distant from it. We formalize this as Controlling Authority Retrieval (CAR): recovering the active frontier front(cl(A_k(q))) of the authority closure of the semantic anchor set -- a different mathematical problem from argmax_d s(q,d). The two central results are: Theorem 4 (CAR-Correctness Characterization) gives necessary-and-sufficient conditions on any retrieved set R for TCA(R,q)=1 -- frontier inclusion and no-ignored-superseder -- independent of how R was produced. Proposition 2 (Scope Identifiability Upper Bound) establishes phi(q) as a hard worst-case ceiling: for any scope-indexed algorithm, TCA@k <= phi(q) * R_anchor(q), proved by an adversarial permutation argument. Three independent real-world corpora validate the proved structure: security advisories (Dense TCA@5=0.270, two-stage 0.975), SCOTUS overruling pairs (Dense=0.172, two-stage 0.926), FDA drug records (Dense=0.064, two-stage 0.774). A GPT-4o-mini experiment shows the downstream cost: Dense RAG produces explicit "not patched" claims for 39% of queries where a patch exists; Two-Stage cuts this to 16%. Four benchmark datasets, domain adapters, and a single-command scorer are released at this https URL.
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URL
https://arxiv.org/abs/2604.14488
