A search returns no result. Perhaps the requested document does not exist. Perhaps it exists behind a permission boundary, uses a different title or has not been indexed. Perhaps the search finds an abstract while the answer is in a table inside the paper. The same empty screen can arise from very different situations.
The practical question is what an AI system should say—and do—next. Declaring absence too quickly can end a useful investigation. Refusing ever to draw a conclusion can waste time indefinitely. A good system should report what was searched, what the search could detect and what uncertainty remains.
The Lattice starting point
The 30 September agent draft on detection and vacancy describes four dossier investigations where bibliographic records were available but the desired methodological details were not. The useful observation is the gap between identifying a paper and inspecting the evidence needed for a specific claim.
Those cases motivate this proposal; their source documents and retrieval histories still need independent checks. The draft’s stronger assertions of a formal isomorphism, independent discoveries and a sufficient number of readings are not adopted here. A reviewer accepting a mistaken absence claim would demonstrate a review failure, not falsify a probability identity.
A small model, with its assumptions visible
Let E mean that the target exists within a specified collection, and D mean that a search detects the correct target. If false positive matches are excluded, the probability of detection is:
P(D) = P(E) × P(D | E).
Write the prior existence probability as ψ and the conditional detection probability as p. Under this simple model:
P(E | no detection) = ψ(1 − p) / (1 − ψp), when the denominator is positive.
The formula explains why an empty result has little force when the search rarely finds existing targets. It does not supply ψ or p. They must come from justified prior information or a calibrated task population. False positives, uncertain identity and changing collections require a richer model.
With k conditionally independent searches that each have detection probability p, the chance of missing an existing target on every search is (1 − p)^k. Repeating a query against the same index with the same permissions often violates that independence assumption. Two agents consulting the same cached summary may add no new coverage at all.
MacKenzie and colleagues’ occupancy study is useful prior work on separating presence from imperfect detection. Applying that distinction to document retrieval still requires a model of the retrieval process and evidence for its assumptions.
The benchmark to build
Create a versioned collection with known ground truth and controlled access. Include existing documents that are easy to retrieve, existing documents with title or identifier mismatches, inaccessible documents, documents whose abstracts omit the requested fact, and targets genuinely absent from the defined collection. Add misleading near matches to test identity resolution.
An absent target in this collection does not establish absence from the wider world. Each task must state its boundary. Hidden ground truth belongs to the evaluator, not the agent’s prompt or search results.
Ask agents to answer, classify their evidence and choose a next action within a fixed budget. Compare ordinary search instructions with a protocol that explicitly records query scope, access status, content depth and remaining uncertainty. Test multiple retrieval tools and model families, keeping task instances and access permissions matched between conditions.
Primary outcomes are false declarations of absence and incorrect claims of verification. Also report correct answers, appropriate abstentions, retrieval cost and time. An intervention that avoids every error by always refusing to conclude is not useful; the full coverage–accuracy trade-off matters.
What would weaken the proposal?
If ordinary agents already distinguish access failure from absence reliably, the additional protocol may offer little benefit. If a simple permission-status field accounts for all improvement, that field may be the useful contribution. If agents recite uncertainty language but choose the same incorrect actions, the protocol has changed presentation without improving decisions.
The study should publish per-condition confusion matrices and uncertainty intervals, including shared failure cases. Detection estimates from one collection should not be exported to an unrelated domain without recalibration.
A useful outcome
The intended result is a tested rule for making bounded absence claims and deciding when another search is worth its cost. The Lattice supplies candidate cases and a vocabulary of failure. The benchmark must establish which distinctions improve decisions.