Controlling Authority Retrieval: A Missing Retrieval Objective for Authority-Governed Knowledge
Abstract
In law, regulatory regimes for pharmaceuticals and software security, newer authorities can revoke older established ones even when semantically distant. We call this CAR: retrieving the currently active authority frontier for a semantic anchor q, that is, front(cl(A_k(q))). This differs from finding the most similar document by relevance score: argmax_d s(q, d). Theorem 4 characterizes when a set R truly covers the active authority set for q with TCA(R, q)=1, providing conditions necessary and sufficient for any retrieved set R: frontier inclusion (front(cl(A_k(q))) contained in R) and no-ignored-superseder (no superseding document exists in the corpus outside R). Proposition 2 shows that TCA@k <= phi(q) * R_anchor(q) in the worst case over any scope-indexed algorithm, proved by an adversarial permutation argument. We evaluated on three real-world datasets: security advisories (Dense TCA@5=0.270, two-stage 0.975), SCOTUS overruling pairs (Dense TCA=0.172, two-stage 0.926), and FDA drug records (Dense TCA=0.064, two-stage 0.774). A GPT-4o-mini experiment shows 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 https://github.com/andremir/car-retrieval.
Figures & tables
| Result | Role | Claim (independent of pipeline) |
|---|---|---|
| Theorem 4 | Correctness | N&S conditions on any : frontier inclusion no-ignored-superseder |
| Proposition 2 | Limit | Hard worst-case ceiling on all scope-indexed algorithms |
| Theorem 3 Cor. 3 | Construction | Two-stage is sufficient when ; T1, T2 prove each component necessary |
| Proposition 3 | Cost | oracle lower bound; RSSG costs without oracle |
| Theorems 1–2, P1, L1 | Context / synthesis | Mismatch, closure necessity, factorization, separability |
| T0 | T1 | T2 | T3 | |
|---|---|---|---|---|
| Examples | 250 | 250 | 250 | 250 |
| KB events (avg) | 1.0 | 2.0 | 3.0 | 3.0 |
| Supersession hops | 0 | 1 | 2 | 2 |
| Cross-provenance | No | No | No | Yes |
| Shared retrieval corpus: 12,250 events total | ||||
| Overall | TCA by Hop Type | |||||||
| System | R@5 | TCA | Acc | ProvRec | T0 | T1 | T2 | T3 |
| BM25 | 0.607 | 0.305 | 0.503 | 0.607 | 1.000 | 0.000 | 0.216 | 0.004 |
| TF-IDF (cosine) | 0.621 | 0.254 | 0.491 | 0.621 | 1.000 | 0.000 | 0.012 | 0.004 |
| Dense (MiniLM) | 0.450 | 0.214 | 0.247 | 0.450 | 0.820 | 0.000 | 0.036 | 0.000 |
| Oracle | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| DenseReRank | 0.333 | 0.499 | 0.499 | 0.333 | 1.000 | 0.000 | 0.980 | 0.016 |
| System | TCA | T3 | T3 |
|---|---|---|---|
| TwoStage (anchor only) | 0.911 | 0.652 | — |
| TwoStage+RSSG (anchor + RSSG) | 0.942 | 0.776 | pp |
| Metric | Query Disclosure | Query Patch |
|---|---|---|
| Jaccard | 0.085 | 0.060 |
| Jaccard (no stopwords) | 0.037 | 0.014 |
| % positive gap (Jaccard) | 96.7% | — |
| BM25 score | 9.73 | 6.45 |
| % positive gap (BM25) | 97.5% | — |
| System | TCA@5 | TCA@10 | TCA@20 | Mean rank | Median rank |
|---|---|---|---|---|---|
| BM25 | 0.641 | 0.730 | 0.761 | 144.4 | 3 |
| Dense (MiniLM) | 0.132 | 0.157 | 0.214 | 1,234 | 1,847 |
| Dense (E5-large) | 0.069 | 0.120 | 0.170 | 1,113 | 1,246 |
| HyDE (Llama 3.3 70B) | 0.151 | 0.170 | 0.170 | 1,283 | 1,577 |
| Regex-NER Probe | 1.000 | 1.000 | 1.000 | 2.0 | 2 |
| System | Disc@5 | TCA@5 | TCA@10 | Mean rank |
|---|---|---|---|---|
| BM25 | 0.975 | 0.138 | 0.214 | 609 |
| Dense (MiniLM) | 0.937 | 0.270 | 0.365 | 764 |
| Dense (E5-large) | 0.962 | 0.252 | 0.321 | 799 |
| HyDE (Llama 3.3 70B) | — | 0.151 | — | — |
| Two-Stage ( ) | 0.975 | 0.975 | — | 43.2 |
| Model | Params | Family | Disc@5 | TCA@5 |
| MiniLM-L6-v2 | 22M | MiniLM | 0.962 | 0.283 |
| E5-small-v2 | 33M | E5 | 0.987 | 0.264 |
| E5-base-v2 | 109M | E5 | 0.950 | 0.239 |
| E5-large-v2 | 335M | E5 | 0.956 | 0.214 |
| BGE-small | 33M | BGE | 0.981 | 0.252 |
| BGE-base | 109M | BGE | 0.975 | 0.283 |
| Domain | Query style | Stage-1 Rec@5 | BM25 | Two-Stage |
|---|---|---|---|---|
| Security (real, ) | Generic free-form | 0.975 | 0.138 | 0.975 |
| CVE (synth, ) | Generic free-form | 0.860 | 0.000 | 0.860 |
| CVE (synth, ) | + product hint | 1.000 † | 0.000 | 0.900 |
| Legal (synth, ) | Generic free-form | 0.312 | 0.000 | 0.312 |
| Legal (synth, ) | + party-name hint | 1.000 | 0.000 | 1.000 |
| System | Finance T1 | CVE T1 | Legal T1 |
|---|---|---|---|
| BM25 / TF-IDF | 0.000 | 0.000 | 0.000 |
| TwoStage | 1.000 | 1.000 | 1.000 |
| TwoStage+RSSG | 1.000 | 1.000 | 1.000 |
| System | Anchor@5 | TCA@5 | 95% CI |
|---|---|---|---|
| BM25 direct | — | 0.893 | [0.826, 0.936] |
| Dense (MiniLM) direct | — | 0.172 | [0.115, 0.249] |
| Two-Stage (BM25 anchor) | 0.836 | 0.836 | [0.760, 0.891] |
| Two-Stage (Dense anchor) | 0.926 | 0.926 | [0.865, 0.961] |
| System | Stage-1 @5 | TCA@5 | 95% CI |
|---|---|---|---|
| BM25 direct | — | 0.004 | [0.001, 0.014] |
| Dense (MiniLM) direct | — | 0.064 | [0.046, 0.089] |
| Two-Stage (BM25 anchor) | 0.774 | 0.774 | [0.735, 0.808] |
| Condition | Patch Recall@5 | Says Patched | Conf. Wrong | Uncertain |
|---|---|---|---|---|
| Dense (MiniLM) | 28.3% | 61.0% | 39.0% | 0% |
| Two-Stage (BM25) | 97.5% | 82.4% | 16.4% | 1% |
| Domain | n | BM25 | Dense | Two-Stage | vs. Dense |
|---|---|---|---|---|---|
| Security (GHSA) | 159 | 0.138 | 0.270 | 0.975 | pp |
| Legal (SCOTUS LII) | 122 | 0.893 | 0.172 | 0.926 | pp |
| Medical (FDA Recall) | 500 | 0.004 | 0.064 | 0.774 | pp |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| Rule | Trigger | Target | Scope |
|---|---|---|---|
| R1 | BlackoutAnnounced | PreClearanceApproved | Same ticker |
| R2 | BlackoutLifted | BlackoutAnnounced | Same ticker |
| R3 | EmergencyException | BlackoutAnnounced | Emp + ticker |
| R4 | ExceptionRevoked | EmergencyException | Emp + ticker |
| R5 | WatchlistAdded | PreClearanceApproved | Same ticker |
| R6 | WatchlistRemoved | WatchlistAdded | Same ticker |
Legal IR
Legal information retrieval finds and ranks relevant statutes, cases, patents, and other legal materials for queries and evidence-grounded systems.
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