{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AOO6FF4S7MZXTQW5L6RCUMJLF7","short_pith_number":"pith:AOO6FF4S","schema_version":"1.0","canonical_sha256":"039de29792fb3379c2dd5fa22a312b2fd55111b569435bd829081d36c62dfcfd","source":{"kind":"arxiv","id":"1703.07521","version":5},"attestation_state":"computed","paper":{"title":"Lifting randomized query complexity to randomized communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Naresh B. Goud, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu","submitted_at":"2017-03-22T04:45:51Z","abstract_excerpt":"We show that for a relation $f\\subseteq \\{0,1\\}^n\\times \\mathcal{O}$ and a function $g:\\{0,1\\}^{m}\\times \\{0,1\\}^{m} \\rightarrow \\{0,1\\}$ (with $m= O(\\log n)$), $$\\mathrm{R}_{1/3}(f\\circ g^n) = \\Omega\\left(\\mathrm{R}_{1/3}(f) \\cdot \\left(\\log\\frac{1}{\\mathrm{disc}(M_g)} - O(\\log n)\\right)\\right),$$ where $f\\circ g^n$ represents the composition of $f$ and $g^n$, $M_g$ is the sign matrix for $g$, $\\mathrm{disc}(M_g)$ is the discrepancy of $M_g$ under the uniform distribution and $\\mathrm{R}_{1/3}(f)$ ($\\mathrm{R}_{1/3}(f\\circ g^n)$) denotes the randomized query complexity of $f$ (randomized comm"},"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":"1703.07521","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-22T04:45:51Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"fcf101f61009e2a1ecd1e285d7aec296e430c1a046807e5c6012f2f24cfa5dd5","abstract_canon_sha256":"51c7b8f915d5a81388840c6dd7493a0716d36e905ec125bab969b1fc4d8d448c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:29.144765Z","signature_b64":"+hnHDxuMiFfLhvZhaNGQZFVRSvDUkfoPK/PvWUNVwwnCgeWP4BFcU6lwF3Wf1gfWQ1sKi0vkkMULtB4JN6uYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"039de29792fb3379c2dd5fa22a312b2fd55111b569435bd829081d36c62dfcfd","last_reissued_at":"2026-05-18T00:25:29.144166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:29.144166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting randomized query complexity to randomized communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Naresh B. Goud, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu","submitted_at":"2017-03-22T04:45:51Z","abstract_excerpt":"We show that for a relation $f\\subseteq \\{0,1\\}^n\\times \\mathcal{O}$ and a function $g:\\{0,1\\}^{m}\\times \\{0,1\\}^{m} \\rightarrow \\{0,1\\}$ (with $m= O(\\log n)$), $$\\mathrm{R}_{1/3}(f\\circ g^n) = \\Omega\\left(\\mathrm{R}_{1/3}(f) \\cdot \\left(\\log\\frac{1}{\\mathrm{disc}(M_g)} - O(\\log n)\\right)\\right),$$ where $f\\circ g^n$ represents the composition of $f$ and $g^n$, $M_g$ is the sign matrix for $g$, $\\mathrm{disc}(M_g)$ is the discrepancy of $M_g$ under the uniform distribution and $\\mathrm{R}_{1/3}(f)$ ($\\mathrm{R}_{1/3}(f\\circ g^n)$) denotes the randomized query complexity of $f$ (randomized comm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07521","kind":"arxiv","version":5},"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":"1703.07521","created_at":"2026-05-18T00:25:29.144256+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07521v5","created_at":"2026-05-18T00:25:29.144256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07521","created_at":"2026-05-18T00:25:29.144256+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOO6FF4S7MZX","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOO6FF4S7MZXTQW5","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOO6FF4S","created_at":"2026-05-18T12:31:05.417338+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/AOO6FF4S7MZXTQW5L6RCUMJLF7","json":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7.json","graph_json":"https://pith.science/api/pith-number/AOO6FF4S7MZXTQW5L6RCUMJLF7/graph.json","events_json":"https://pith.science/api/pith-number/AOO6FF4S7MZXTQW5L6RCUMJLF7/events.json","paper":"https://pith.science/paper/AOO6FF4S"},"agent_actions":{"view_html":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7","download_json":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7.json","view_paper":"https://pith.science/paper/AOO6FF4S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07521&json=true","fetch_graph":"https://pith.science/api/pith-number/AOO6FF4S7MZXTQW5L6RCUMJLF7/graph.json","fetch_events":"https://pith.science/api/pith-number/AOO6FF4S7MZXTQW5L6RCUMJLF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7/action/storage_attestation","attest_author":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7/action/author_attestation","sign_citation":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7/action/citation_signature","submit_replication":"https://pith.science/pith/AOO6FF4S7MZXTQW5L6RCUMJLF7/action/replication_record"}},"created_at":"2026-05-18T00:25:29.144256+00:00","updated_at":"2026-05-18T00:25:29.144256+00:00"}