{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:DBEI55QC7RWIMP7SPB2P577FGN","short_pith_number":"pith:DBEI55QC","schema_version":"1.0","canonical_sha256":"18488ef602fc6c863ff27874feffe53342ee2c1f4c8f1e727356a990e2caeed3","source":{"kind":"arxiv","id":"2008.07188","version":3},"attestation_state":"computed","paper":{"title":"A near-optimal direct-sum theorem for communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rahul Jain","submitted_at":"2020-08-17T10:04:08Z","abstract_excerpt":"We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\\subseteq X \\times Y\\times Z$ be a relation, $\\varepsilon> 0$ and $k$ be an integer. We show, $$\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k) \\cdot \\log(\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k)) \\ge \\Omega(k \\cdot \\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f)) \\enspace,$$ where $f^k= f \\times \\ldots \\times f$ ($k$-times) and $\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(\\cdot)$ represents the public-coin randomized communication complexity with worst-case error $\\varepsilon$. Given a protocol $\\mathcal{P}"},"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":"2008.07188","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-08-17T10:04:08Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1004f3ee00bda0c0e333018ddcea0d3efbe36f2290463df2d5d31868006e30ab","abstract_canon_sha256":"af3274c32c245d4bd59a0a626379c3705f9381a7c5a1fa548dad930cb41736e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:32:46.640889Z","signature_b64":"18bGINEGGmhp2Er2e5CjGJuEhTS01IXHpB9LTB9EwSgWEdJC0+Mwb2cOwkaa5t6H1dd9RFx1KH30WJRC/sguCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18488ef602fc6c863ff27874feffe53342ee2c1f4c8f1e727356a990e2caeed3","last_reissued_at":"2026-07-05T01:32:46.640440Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:32:46.640440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A near-optimal direct-sum theorem for communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rahul Jain","submitted_at":"2020-08-17T10:04:08Z","abstract_excerpt":"We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\\subseteq X \\times Y\\times Z$ be a relation, $\\varepsilon> 0$ and $k$ be an integer. We show, $$\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k) \\cdot \\log(\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f^k)) \\ge \\Omega(k \\cdot \\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(f)) \\enspace,$$ where $f^k= f \\times \\ldots \\times f$ ($k$-times) and $\\mathrm{R}^{\\mathrm{pub}}_\\varepsilon(\\cdot)$ represents the public-coin randomized communication complexity with worst-case error $\\varepsilon$. Given a protocol $\\mathcal{P}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.07188/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2008.07188","created_at":"2026-07-05T01:32:46.640497+00:00"},{"alias_kind":"arxiv_version","alias_value":"2008.07188v3","created_at":"2026-07-05T01:32:46.640497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07188","created_at":"2026-07-05T01:32:46.640497+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBEI55QC7RWI","created_at":"2026-07-05T01:32:46.640497+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBEI55QC7RWIMP7S","created_at":"2026-07-05T01:32:46.640497+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBEI55QC","created_at":"2026-07-05T01:32:46.640497+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/DBEI55QC7RWIMP7SPB2P577FGN","json":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN.json","graph_json":"https://pith.science/api/pith-number/DBEI55QC7RWIMP7SPB2P577FGN/graph.json","events_json":"https://pith.science/api/pith-number/DBEI55QC7RWIMP7SPB2P577FGN/events.json","paper":"https://pith.science/paper/DBEI55QC"},"agent_actions":{"view_html":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN","download_json":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN.json","view_paper":"https://pith.science/paper/DBEI55QC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2008.07188&json=true","fetch_graph":"https://pith.science/api/pith-number/DBEI55QC7RWIMP7SPB2P577FGN/graph.json","fetch_events":"https://pith.science/api/pith-number/DBEI55QC7RWIMP7SPB2P577FGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN/action/storage_attestation","attest_author":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN/action/author_attestation","sign_citation":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN/action/citation_signature","submit_replication":"https://pith.science/pith/DBEI55QC7RWIMP7SPB2P577FGN/action/replication_record"}},"created_at":"2026-07-05T01:32:46.640497+00:00","updated_at":"2026-07-05T01:32:46.640497+00:00"}