{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6ZLF7G26JORFQ55CAA523TLFUX","short_pith_number":"pith:6ZLF7G26","schema_version":"1.0","canonical_sha256":"f6565f9b5e4ba25877a2003badcd65a5cb85bd29bc1b791b65f17dc1e270f4bf","source":{"kind":"arxiv","id":"1706.00335","version":2},"attestation_state":"computed","paper":{"title":"A Composition Theorem for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Dmitry Gavinsky, Miklos Santha, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu, Swagato Sanyal, Troy Lee","submitted_at":"2017-06-01T15:09:27Z","abstract_excerpt":"Let the randomized query complexity of a relation for error probability $\\epsilon$ be denoted by $R_\\epsilon(\\cdot)$. We prove that for any relation $f \\subseteq \\{0,1\\}^n \\times \\mathcal{R}$ and Boolean function $g:\\{0,1\\}^m \\rightarrow \\{0,1\\}$, $R_{1/3}(f\\circ g^n) = \\Omega(R_{4/9}(f)\\cdot R_{1/2-1/n^4}(g))$, where $f \\circ g^n$ is the relation obtained by composing $f$ and $g$. We also show that $R_{1/3}\\left(f \\circ \\left(g^\\oplus_{O(\\log n)}\\right)^n\\right)=\\Omega(\\log n \\cdot R_{4/9}(f) \\cdot R_{1/3}(g))$, where $g^\\oplus_{O(\\log n)}$ is the function obtained by composing the xor functi"},"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":"1706.00335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-06-01T15:09:27Z","cross_cats_sorted":[],"title_canon_sha256":"5f65b094669888ed1d8067175a630c4e18c463f54c208eb33255c85a367fed24","abstract_canon_sha256":"674c2d2aca4ae32f01b87a34944872d2b91c503d2bb97888ab31bdeab9b44bae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:23.309146Z","signature_b64":"4JMtUct4xbVpxd+2YvgUBrZ/aFPuVdVLHQKXULyNdwODzYcBm5QEoCqnnJa/qZH57Qh1u73s9RHh0ivZB/RyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6565f9b5e4ba25877a2003badcd65a5cb85bd29bc1b791b65f17dc1e270f4bf","last_reissued_at":"2026-05-18T00:42:23.308661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:23.308661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Composition Theorem for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Dmitry Gavinsky, Miklos Santha, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu, Swagato Sanyal, Troy Lee","submitted_at":"2017-06-01T15:09:27Z","abstract_excerpt":"Let the randomized query complexity of a relation for error probability $\\epsilon$ be denoted by $R_\\epsilon(\\cdot)$. We prove that for any relation $f \\subseteq \\{0,1\\}^n \\times \\mathcal{R}$ and Boolean function $g:\\{0,1\\}^m \\rightarrow \\{0,1\\}$, $R_{1/3}(f\\circ g^n) = \\Omega(R_{4/9}(f)\\cdot R_{1/2-1/n^4}(g))$, where $f \\circ g^n$ is the relation obtained by composing $f$ and $g$. We also show that $R_{1/3}\\left(f \\circ \\left(g^\\oplus_{O(\\log n)}\\right)^n\\right)=\\Omega(\\log n \\cdot R_{4/9}(f) \\cdot R_{1/3}(g))$, where $g^\\oplus_{O(\\log n)}$ is the function obtained by composing the xor functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00335","kind":"arxiv","version":2},"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":"1706.00335","created_at":"2026-05-18T00:42:23.308731+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00335v2","created_at":"2026-05-18T00:42:23.308731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00335","created_at":"2026-05-18T00:42:23.308731+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZLF7G26JORF","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZLF7G26JORFQ55C","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZLF7G26","created_at":"2026-05-18T12:31:03.183658+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/6ZLF7G26JORFQ55CAA523TLFUX","json":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX.json","graph_json":"https://pith.science/api/pith-number/6ZLF7G26JORFQ55CAA523TLFUX/graph.json","events_json":"https://pith.science/api/pith-number/6ZLF7G26JORFQ55CAA523TLFUX/events.json","paper":"https://pith.science/paper/6ZLF7G26"},"agent_actions":{"view_html":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX","download_json":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX.json","view_paper":"https://pith.science/paper/6ZLF7G26","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00335&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZLF7G26JORFQ55CAA523TLFUX/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZLF7G26JORFQ55CAA523TLFUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX/action/storage_attestation","attest_author":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX/action/author_attestation","sign_citation":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX/action/citation_signature","submit_replication":"https://pith.science/pith/6ZLF7G26JORFQ55CAA523TLFUX/action/replication_record"}},"created_at":"2026-05-18T00:42:23.308731+00:00","updated_at":"2026-05-18T00:42:23.308731+00:00"}