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For any relation $f \\subseteq \\{0,1\\}^n \\times S$ and partial Boolean function $g \\subseteq \\{0,1\\}^m \\times \\{0,1\\}$, we show that $R_{1/3}(f \\circ g^n) \\in \\Omega(R_{4/9}(f) \\cdot \\sqrt{R_{1/3}(g)})$, where $f \\circ g^n \\subseteq (\\{0,1\\}^m)^n \\times S$ is the composition of $f$ and $g$. We give an example of a relation $f$ and partial Boolean function $g$ for which this lower bound is tight.\n  We prove our composition theorem by introducing a new complexity measure, the max conflict co"},"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":"1811.10752","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2018-11-27T00:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"51fd171753586825ca971b6830e8a9b8762d1828edfc37277330a897842557aa","abstract_canon_sha256":"66ba8854c06f49d227eda217b0551cd6887fc499b4303489746d019ca777f148"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:47.636465Z","signature_b64":"NZn4i3pCU4I4Lqhs4AMcgCI0RtyIxzpiWp6HKIIbW2LsD6mckjDAhBjvznyDLj7dkz/SABm6p8xF/TLHPd0wDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"269a50c94dbaab9f4e7adda3037b06e0b6093c62a735b18d841d080c65c141de","last_reissued_at":"2026-05-17T23:59:47.635980Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:47.635980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A composition theorem for randomized query complexity via max conflict complexity","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dmitry Gavinsky, Miklos Santha, Swagato Sanyal, Troy Lee","submitted_at":"2018-11-27T00:11:08Z","abstract_excerpt":"Let $R_\\epsilon(\\cdot)$ stand for the bounded-error randomized query complexity with error $\\epsilon > 0$. For any relation $f \\subseteq \\{0,1\\}^n \\times S$ and partial Boolean function $g \\subseteq \\{0,1\\}^m \\times \\{0,1\\}$, we show that $R_{1/3}(f \\circ g^n) \\in \\Omega(R_{4/9}(f) \\cdot \\sqrt{R_{1/3}(g)})$, where $f \\circ g^n \\subseteq (\\{0,1\\}^m)^n \\times S$ is the composition of $f$ and $g$. We give an example of a relation $f$ and partial Boolean function $g$ for which this lower bound is tight.\n  We prove our composition theorem by introducing a new complexity measure, the max conflict co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10752","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.10752","created_at":"2026-05-17T23:59:47.636057+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.10752v1","created_at":"2026-05-17T23:59:47.636057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10752","created_at":"2026-05-17T23:59:47.636057+00:00"},{"alias_kind":"pith_short_12","alias_value":"E2NFBSKNXKVZ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"E2NFBSKNXKVZ6TT2","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"E2NFBSKN","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C","json":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C.json","graph_json":"https://pith.science/api/pith-number/E2NFBSKNXKVZ6TT23WRQG6YG4C/graph.json","events_json":"https://pith.science/api/pith-number/E2NFBSKNXKVZ6TT23WRQG6YG4C/events.json","paper":"https://pith.science/paper/E2NFBSKN"},"agent_actions":{"view_html":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C","download_json":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C.json","view_paper":"https://pith.science/paper/E2NFBSKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.10752&json=true","fetch_graph":"https://pith.science/api/pith-number/E2NFBSKNXKVZ6TT23WRQG6YG4C/graph.json","fetch_events":"https://pith.science/api/pith-number/E2NFBSKNXKVZ6TT23WRQG6YG4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C/action/storage_attestation","attest_author":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C/action/author_attestation","sign_citation":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C/action/citation_signature","submit_replication":"https://pith.science/pith/E2NFBSKNXKVZ6TT23WRQG6YG4C/action/replication_record"}},"created_at":"2026-05-17T23:59:47.636057+00:00","updated_at":"2026-05-17T23:59:47.636057+00:00"}