Search that misses nothing — and proves it.

The completeness guarantee

For range and k-NN in L2, SIEVE proves that no neighbor within the radius was left out. Not '99% recall': proven absence — 'I searched everything and none is left', the sentence compliance and forensics buy.

• ▸Forensics: find every case matching a pattern, no false negative.
• ▸Detection: agent doom-loop (literal, cyclic, paraphrastic) with zero false positives, measured on real embeddings.
• ▸Certified absence: 'no record exceeded the cap' = a proven empty range.

Composes with the family

SIEVE ∘ CLAMP = certified aggregate over a certified neighborhood. Proved on real data (327/327, a 2.26 °C bracket = ε + search). Completeness enables attribution, and attribution enables audit.

The honest limit

The claim 'faster than brute force in RAM for L2' was refuted and reported — SIEVE's strength is the guarantee (deterministic zero-FN), not raw speed. We say what we measure.