{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4R4AALM64XCA22R6VHV4YYQIVJ","short_pith_number":"pith:4R4AALM6","schema_version":"1.0","canonical_sha256":"e478002d9ee5c40d6a3ea9ebcc6208aa430fb32aca23dafbc0f6f2e85df51285","source":{"kind":"arxiv","id":"1511.01937","version":2},"attestation_state":"computed","paper":{"title":"Separations in query complexity using cheat sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Robin Kothari, Scott Aaronson, Shalev Ben-David","submitted_at":"2015-11-05T22:31:22Z","abstract_excerpt":"We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method. Finally, we exhibit a total function with a quadratic gap between quantum query complexity and certificate complexity, which is optimal (up to log factors). These "},"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":"1511.01937","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-11-05T22:31:22Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"bdb5b00f3e9b5e02ae10b4ecf41dade9a0d8ac2fab8c843a848e1f9119b56c38","abstract_canon_sha256":"dced25a4144c199d75b2c1e117ddb41e24ade4064ba7b9a943e2c235b0635132"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:13.748597Z","signature_b64":"yhzWC164AX5+E6+xYt05IJGGCmJaaWA0dpRF4Pkw6Utsl2RFWqBu2hpCfciP2O0CJO24h+EcPTss4ssrk3lnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e478002d9ee5c40d6a3ea9ebcc6208aa430fb32aca23dafbc0f6f2e85df51285","last_reissued_at":"2026-05-17T23:41:13.748128Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:13.748128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separations in query complexity using cheat sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Robin Kothari, Scott Aaronson, Shalev Ben-David","submitted_at":"2015-11-05T22:31:22Z","abstract_excerpt":"We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only be quadratic (from Grover's algorithm). We also present a total function with a power 4 separation between quantum query complexity and approximate polynomial degree, showing severe limitations on the power of the polynomial method. Finally, we exhibit a total function with a quadratic gap between quantum query complexity and certificate complexity, which is optimal (up to log factors). These "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01937","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":"1511.01937","created_at":"2026-05-17T23:41:13.748203+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.01937v2","created_at":"2026-05-17T23:41:13.748203+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01937","created_at":"2026-05-17T23:41:13.748203+00:00"},{"alias_kind":"pith_short_12","alias_value":"4R4AALM64XCA","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4R4AALM64XCA22R6","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4R4AALM6","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.04232","citing_title":"Span Programs and Quantum Space Complexity","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ","json":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ.json","graph_json":"https://pith.science/api/pith-number/4R4AALM64XCA22R6VHV4YYQIVJ/graph.json","events_json":"https://pith.science/api/pith-number/4R4AALM64XCA22R6VHV4YYQIVJ/events.json","paper":"https://pith.science/paper/4R4AALM6"},"agent_actions":{"view_html":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ","download_json":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ.json","view_paper":"https://pith.science/paper/4R4AALM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.01937&json=true","fetch_graph":"https://pith.science/api/pith-number/4R4AALM64XCA22R6VHV4YYQIVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/4R4AALM64XCA22R6VHV4YYQIVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ/action/storage_attestation","attest_author":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ/action/author_attestation","sign_citation":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ/action/citation_signature","submit_replication":"https://pith.science/pith/4R4AALM64XCA22R6VHV4YYQIVJ/action/replication_record"}},"created_at":"2026-05-17T23:41:13.748203+00:00","updated_at":"2026-05-17T23:41:13.748203+00:00"}