{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MDKII4D7SI2LPR6DQTHKHWVROT","short_pith_number":"pith:MDKII4D7","schema_version":"1.0","canonical_sha256":"60d484707f9234b7c7c384cea3dab174ce4024598c93df4809acaaa4076a1fb1","source":{"kind":"arxiv","id":"2411.17823","version":3},"attestation_state":"computed","paper":{"title":"Triple sums of Kloosterman sums and the discrepancy of modular inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Morten S. Risager, Valentin Blomer","submitted_at":"2024-11-26T19:02:50Z","abstract_excerpt":"We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums."},"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":"2411.17823","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-11-26T19:02:50Z","cross_cats_sorted":[],"title_canon_sha256":"6daa76899d085bbefd649bb132c63d16d354236f7a2993376f64f5422e8d5c75","abstract_canon_sha256":"afe7731b67803dbaa7adaf01276c5dc12b248f773f7d33cf59cd1e76f1d86984"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:51.191573Z","signature_b64":"e9CPJ0Qd6Ckb5bgwH+TXQ3foVdHarZmiibFeNLTr55hrHO0QDMTLeVds3kme8uRO3KfhduwPNK45pgptIB4ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60d484707f9234b7c7c384cea3dab174ce4024598c93df4809acaaa4076a1fb1","last_reissued_at":"2026-07-05T11:56:51.191141Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:51.191141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Triple sums of Kloosterman sums and the discrepancy of modular inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor E. Shparlinski, Morten S. Risager, Valentin Blomer","submitted_at":"2024-11-26T19:02:50Z","abstract_excerpt":"We investigate the distribution of modular inverses modulo positive integers $c$ in a large interval. We provide upper and lower bounds for their box, ball and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17823","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/2411.17823/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":"2411.17823","created_at":"2026-07-05T11:56:51.191200+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.17823v3","created_at":"2026-07-05T11:56:51.191200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17823","created_at":"2026-07-05T11:56:51.191200+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDKII4D7SI2L","created_at":"2026-07-05T11:56:51.191200+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDKII4D7SI2LPR6D","created_at":"2026-07-05T11:56:51.191200+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDKII4D7","created_at":"2026-07-05T11:56:51.191200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.07951","citing_title":"On denominators of consecutive $\\operatorname{SL}(2,{\\mathbb N})$-saturated Farey fractions","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT","json":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT.json","graph_json":"https://pith.science/api/pith-number/MDKII4D7SI2LPR6DQTHKHWVROT/graph.json","events_json":"https://pith.science/api/pith-number/MDKII4D7SI2LPR6DQTHKHWVROT/events.json","paper":"https://pith.science/paper/MDKII4D7"},"agent_actions":{"view_html":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT","download_json":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT.json","view_paper":"https://pith.science/paper/MDKII4D7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.17823&json=true","fetch_graph":"https://pith.science/api/pith-number/MDKII4D7SI2LPR6DQTHKHWVROT/graph.json","fetch_events":"https://pith.science/api/pith-number/MDKII4D7SI2LPR6DQTHKHWVROT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT/action/storage_attestation","attest_author":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT/action/author_attestation","sign_citation":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT/action/citation_signature","submit_replication":"https://pith.science/pith/MDKII4D7SI2LPR6DQTHKHWVROT/action/replication_record"}},"created_at":"2026-07-05T11:56:51.191200+00:00","updated_at":"2026-07-05T11:56:51.191200+00:00"}