{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EXCDU456BZYUI7V4WQO2PFQKBV","short_pith_number":"pith:EXCDU456","schema_version":"1.0","canonical_sha256":"25c43a73be0e71447ebcb41da7960a0d404c773566510277f67206352f986244","source":{"kind":"arxiv","id":"1011.2738","version":2},"attestation_state":"computed","paper":{"title":"An improved sum-product inequality in fields of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Misha Rudnev","submitted_at":"2010-11-11T19:01:30Z","abstract_excerpt":"This note improves the best known exponent 1/12 in the prime field sum-product inequality (for small sets) to 1/11, modulo a logarithmic factor."},"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":"1011.2738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-11T19:01:30Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c151f8994455820ff62fbc0be663b8d5d30af0e5b34e444faa281e9ab6ba31bb","abstract_canon_sha256":"9ac84a8220e89f78647907ed97ccf963a503d052b0d8639daab9c4d3f8dc5a6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:47.857101Z","signature_b64":"jtaHvVBrJGYutce0x3KCfA01bbGFO0GzInBszrNfkbAK8ybbNFZPZhFZ1jt5GCijn21gCvMOEXtCPBjd/NIbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c43a73be0e71447ebcb41da7960a0d404c773566510277f67206352f986244","last_reissued_at":"2026-05-18T04:23:47.856586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:47.856586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An improved sum-product inequality in fields of prime order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Misha Rudnev","submitted_at":"2010-11-11T19:01:30Z","abstract_excerpt":"This note improves the best known exponent 1/12 in the prime field sum-product inequality (for small sets) to 1/11, modulo a logarithmic factor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2738","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":"1011.2738","created_at":"2026-05-18T04:23:47.856661+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2738v2","created_at":"2026-05-18T04:23:47.856661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2738","created_at":"2026-05-18T04:23:47.856661+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXCDU456BZYU","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXCDU456BZYUI7V4","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXCDU456","created_at":"2026-05-18T12:26:06.534383+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/EXCDU456BZYUI7V4WQO2PFQKBV","json":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV.json","graph_json":"https://pith.science/api/pith-number/EXCDU456BZYUI7V4WQO2PFQKBV/graph.json","events_json":"https://pith.science/api/pith-number/EXCDU456BZYUI7V4WQO2PFQKBV/events.json","paper":"https://pith.science/paper/EXCDU456"},"agent_actions":{"view_html":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV","download_json":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV.json","view_paper":"https://pith.science/paper/EXCDU456","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2738&json=true","fetch_graph":"https://pith.science/api/pith-number/EXCDU456BZYUI7V4WQO2PFQKBV/graph.json","fetch_events":"https://pith.science/api/pith-number/EXCDU456BZYUI7V4WQO2PFQKBV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV/action/storage_attestation","attest_author":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV/action/author_attestation","sign_citation":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV/action/citation_signature","submit_replication":"https://pith.science/pith/EXCDU456BZYUI7V4WQO2PFQKBV/action/replication_record"}},"created_at":"2026-05-18T04:23:47.856661+00:00","updated_at":"2026-05-18T04:23:47.856661+00:00"}