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Here we think of $d$ as fixed whereas $n$ is thought of as tending to infinity, and the base of the logarithm is $2$.\n  Translated into the language of combinatorial search theory, this tells us that \\[\n  d \\log n+O(1) \\] queries suffice to identify up to $d$ marked it"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.06164","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-20T00:00:46Z","cross_cats_sorted":[],"title_canon_sha256":"de13bb1c9aa938a3625bbc8361cb8c429bf3e366d2b1820218edac95a0214285","abstract_canon_sha256":"7d4c12d0d288b8e5354570411b31d14d3dfda07981425f0399f7191ebb6aa877"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:50.133372Z","signature_b64":"6rI/Kr1ixxCXLvWixWDFbcykIo8J9IDFDIjjbce25J8gDu9mCaqJUhWv7gX3URaiR83L/31RNIs0OzGE3i8SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d428b5d195c085b8f3f6ea27e4ce819e1a9ca08c9d22eadd90d416ce954f5fcc","last_reissued_at":"2026-05-18T01:18:50.132795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:50.132795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The parity search problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher","submitted_at":"2016-03-20T00:00:46Z","abstract_excerpt":"We prove that for any positive integers $n$ and $d$ there exists a collection consisting of $f=d\\log n+O(1)$ subsets $A_1, A_2, \\ldots, A_f$ of $[n]$ such that for any two distinct subsets $X$ and $Y$ of $[n]$ whose size is at most $d$ there is an index $i\\in [f]$ for which $| A_i\\cap X|$ and $|A_i\\cap Y|$ have different parity. 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