{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:T4BK6DWTOEUJL265J2BB7WFO3P","short_pith_number":"pith:T4BK6DWT","schema_version":"1.0","canonical_sha256":"9f02af0ed3712895ebdd4e821fd8aedbd3efda11b6c73b579f746d0f20119edb","source":{"kind":"arxiv","id":"1510.07980","version":1},"attestation_state":"computed","paper":{"title":"Sums of fractions modulo $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. A. D\\'iaz, M. Z. Garaev","submitted_at":"2015-10-27T16:45:12Z","abstract_excerpt":"Let $\\F_p$ be the field of residue classes modulo a large prime $p$. The present paper is devoted to the problem of representability of elements of $\\F_p$ as sums of fractions of the form $x/y$ with $x,y$ from short intervals of $\\F_p$."},"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":"1510.07980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-27T16:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"95d562905258a46ecb62d6f233087b39d145a339cf81dc9ce7bc066217a2ef01","abstract_canon_sha256":"b6e23f0f59da1529f304d1c9220bb33e79f5bce1f62f716826e2642605b1f705"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:44.918001Z","signature_b64":"HLElg1jICEuh35RCUdRhOd5/Eps0qtEgFZAuKYousCI2NvbvmmeozSI54a1h4lB420LAvXwlOHF9TJ/IRLK9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f02af0ed3712895ebdd4e821fd8aedbd3efda11b6c73b579f746d0f20119edb","last_reissued_at":"2026-05-18T01:28:44.917584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:44.917584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sums of fractions modulo $p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. A. D\\'iaz, M. Z. Garaev","submitted_at":"2015-10-27T16:45:12Z","abstract_excerpt":"Let $\\F_p$ be the field of residue classes modulo a large prime $p$. The present paper is devoted to the problem of representability of elements of $\\F_p$ as sums of fractions of the form $x/y$ with $x,y$ from short intervals of $\\F_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07980","kind":"arxiv","version":1},"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":"1510.07980","created_at":"2026-05-18T01:28:44.917636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.07980v1","created_at":"2026-05-18T01:28:44.917636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07980","created_at":"2026-05-18T01:28:44.917636+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4BK6DWTOEUJ","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4BK6DWTOEUJL265","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4BK6DWT","created_at":"2026-05-18T12:29:42.218222+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/T4BK6DWTOEUJL265J2BB7WFO3P","json":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P.json","graph_json":"https://pith.science/api/pith-number/T4BK6DWTOEUJL265J2BB7WFO3P/graph.json","events_json":"https://pith.science/api/pith-number/T4BK6DWTOEUJL265J2BB7WFO3P/events.json","paper":"https://pith.science/paper/T4BK6DWT"},"agent_actions":{"view_html":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P","download_json":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P.json","view_paper":"https://pith.science/paper/T4BK6DWT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.07980&json=true","fetch_graph":"https://pith.science/api/pith-number/T4BK6DWTOEUJL265J2BB7WFO3P/graph.json","fetch_events":"https://pith.science/api/pith-number/T4BK6DWTOEUJL265J2BB7WFO3P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P/action/storage_attestation","attest_author":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P/action/author_attestation","sign_citation":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P/action/citation_signature","submit_replication":"https://pith.science/pith/T4BK6DWTOEUJL265J2BB7WFO3P/action/replication_record"}},"created_at":"2026-05-18T01:28:44.917636+00:00","updated_at":"2026-05-18T01:28:44.917636+00:00"}