{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AOO6FF4S7MZXTQW5L6RCUMJLF7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"51c7b8f915d5a81388840c6dd7493a0716d36e905ec125bab969b1fc4d8d448c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-22T04:45:51Z","title_canon_sha256":"fcf101f61009e2a1ecd1e285d7aec296e430c1a046807e5c6012f2f24cfa5dd5"},"schema_version":"1.0","source":{"id":"1703.07521","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07521","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07521v5","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07521","created_at":"2026-05-18T00:25:29Z"},{"alias_kind":"pith_short_12","alias_value":"AOO6FF4S7MZX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AOO6FF4S7MZXTQW5","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AOO6FF4S","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:417de8f97e0d4144d796ec1cb7e2092f0641892ceb3604ba76e60c926eaa2e60","target":"graph","created_at":"2026-05-18T00:25:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Anurag Anshu, Naresh B. Goud, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-22T04:45:51Z","title":"Lifting randomized query complexity to randomized communication complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07521","kind":"arxiv","version":5},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9b40954942f85715932af05aa6db2b9343d813ba288de551a036b006994fe254","target":"record","created_at":"2026-05-18T00:25:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"51c7b8f915d5a81388840c6dd7493a0716d36e905ec125bab969b1fc4d8d448c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-03-22T04:45:51Z","title_canon_sha256":"fcf101f61009e2a1ecd1e285d7aec296e430c1a046807e5c6012f2f24cfa5dd5"},"schema_version":"1.0","source":{"id":"1703.07521","kind":"arxiv","version":5}},"canonical_sha256":"039de29792fb3379c2dd5fa22a312b2fd55111b569435bd829081d36c62dfcfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"039de29792fb3379c2dd5fa22a312b2fd55111b569435bd829081d36c62dfcfd","first_computed_at":"2026-05-18T00:25:29.144166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:29.144166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+hnHDxuMiFfLhvZhaNGQZFVRSvDUkfoPK/PvWUNVwwnCgeWP4BFcU6lwF3Wf1gfWQ1sKi0vkkMULtB4JN6uYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:29.144765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07521","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b40954942f85715932af05aa6db2b9343d813ba288de551a036b006994fe254","sha256:417de8f97e0d4144d796ec1cb7e2092f0641892ceb3604ba76e60c926eaa2e60"],"state_sha256":"05606db28a2cfa2bb561789b041d87050dd81dc486968de27b416f25e4a0d01a"}