{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OT5VDXHUMO23UPDYUUPSKZAYHF","short_pith_number":"pith:OT5VDXHU","schema_version":"1.0","canonical_sha256":"74fb51dcf463b5ba3c78a51f25641839642b95dc70c53ec74ea2b56dff73fa5e","source":{"kind":"arxiv","id":"1009.3460","version":3},"attestation_state":"computed","paper":{"title":"An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.CC","authors_text":"Amit Chakrabarti, Oded Regev","submitted_at":"2010-09-17T15:53:26Z","abstract_excerpt":"We prove an optimal $\\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model for a number of fundamental problems, including the estimation of frequency moments.\n  The Gap-Hamming-Distance problem is a communication problem, wherein Alice and Bob receive $n$-bit strings $x$ and $y$, respectively. They are promised that the Hamming distance between $x$ and $y$ is either at least $n/2+\\sqrt{n}$ or at most $n/2-\\sqrt{n}$, and their goal"},"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":"1009.3460","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2010-09-17T15:53:26Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"a49d574e785421b13597fe1447186c91c718a792c7ab38cc370e2589d73919ec","abstract_canon_sha256":"9b9187348e737fdba683b49c876325a77573732aca0d094a67aead08a0ee8ebd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:15.178159Z","signature_b64":"ID8tkKCI6sfMSbuPOR9FvhUqOgdRVwPbTK6H8XLfHBXnk0RL8whenkCrmxaBOVWMSHSag7r7Gcj0BnOpmDK7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74fb51dcf463b5ba3c78a51f25641839642b95dc70c53ec74ea2b56dff73fa5e","last_reissued_at":"2026-05-18T03:52:15.177614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:15.177614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.CC","authors_text":"Amit Chakrabarti, Oded Regev","submitted_at":"2010-09-17T15:53:26Z","abstract_excerpt":"We prove an optimal $\\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model for a number of fundamental problems, including the estimation of frequency moments.\n  The Gap-Hamming-Distance problem is a communication problem, wherein Alice and Bob receive $n$-bit strings $x$ and $y$, respectively. They are promised that the Hamming distance between $x$ and $y$ is either at least $n/2+\\sqrt{n}$ or at most $n/2-\\sqrt{n}$, and their goal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3460","kind":"arxiv","version":3},"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":"1009.3460","created_at":"2026-05-18T03:52:15.177696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3460v3","created_at":"2026-05-18T03:52:15.177696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3460","created_at":"2026-05-18T03:52:15.177696+00:00"},{"alias_kind":"pith_short_12","alias_value":"OT5VDXHUMO23","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OT5VDXHUMO23UPDY","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OT5VDXHU","created_at":"2026-05-18T12:26:12.377268+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/OT5VDXHUMO23UPDYUUPSKZAYHF","json":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF.json","graph_json":"https://pith.science/api/pith-number/OT5VDXHUMO23UPDYUUPSKZAYHF/graph.json","events_json":"https://pith.science/api/pith-number/OT5VDXHUMO23UPDYUUPSKZAYHF/events.json","paper":"https://pith.science/paper/OT5VDXHU"},"agent_actions":{"view_html":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF","download_json":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF.json","view_paper":"https://pith.science/paper/OT5VDXHU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3460&json=true","fetch_graph":"https://pith.science/api/pith-number/OT5VDXHUMO23UPDYUUPSKZAYHF/graph.json","fetch_events":"https://pith.science/api/pith-number/OT5VDXHUMO23UPDYUUPSKZAYHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF/action/storage_attestation","attest_author":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF/action/author_attestation","sign_citation":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF/action/citation_signature","submit_replication":"https://pith.science/pith/OT5VDXHUMO23UPDYUUPSKZAYHF/action/replication_record"}},"created_at":"2026-05-18T03:52:15.177696+00:00","updated_at":"2026-05-18T03:52:15.177696+00:00"}