{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:PBMFKL2RIMEN6ZPO4V2N5IMMMN","short_pith_number":"pith:PBMFKL2R","schema_version":"1.0","canonical_sha256":"7858552f514308df65eee574dea18c637ca83355911b40be808d93a8436ca860","source":{"kind":"arxiv","id":"0902.4332","version":3},"attestation_state":"computed","paper":{"title":"The distribution of the number of points modulo an integer on elliptic curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Hendrik Hubrechts, Wouter Castryck","submitted_at":"2009-02-25T10:06:25Z","abstract_excerpt":"Let F be a finite field and let b and N be integers. We prove explicit estimates for the probability that the number of rational points on a randomly chosen elliptic curve E over F equals b modulo N. The underlying tool is an equidistribution result on the action of Frobenius on the N-torsion subgroup of E. Our results subsume and extend previous work by Achter and Gekeler."},"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":"0902.4332","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-02-25T10:06:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ef2dd00edad2134f697d27593ea63c4b6082f3bae3d8ccdd790518b3f42545fb","abstract_canon_sha256":"0f2a774419636926dc9e9c2654098dcdba2e72f5afff0e17bc2a60ca7c5e4776"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:26.682882Z","signature_b64":"+Ru9NCIAQAZoAh0H+ZczBb80XNYukRXMN0XkBFP7y9AvVE0tZ98brW+MaeOa7CSaitB4e9BK9h76wNSAe6NrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7858552f514308df65eee574dea18c637ca83355911b40be808d93a8436ca860","last_reissued_at":"2026-05-18T04:30:26.682494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:26.682494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The distribution of the number of points modulo an integer on elliptic curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Hendrik Hubrechts, Wouter Castryck","submitted_at":"2009-02-25T10:06:25Z","abstract_excerpt":"Let F be a finite field and let b and N be integers. We prove explicit estimates for the probability that the number of rational points on a randomly chosen elliptic curve E over F equals b modulo N. The underlying tool is an equidistribution result on the action of Frobenius on the N-torsion subgroup of E. Our results subsume and extend previous work by Achter and Gekeler."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4332","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":""},"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":"0902.4332","created_at":"2026-05-18T04:30:26.682550+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.4332v3","created_at":"2026-05-18T04:30:26.682550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4332","created_at":"2026-05-18T04:30:26.682550+00:00"},{"alias_kind":"pith_short_12","alias_value":"PBMFKL2RIMEN","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PBMFKL2RIMEN6ZPO","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PBMFKL2R","created_at":"2026-05-18T12:26:01.383474+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/PBMFKL2RIMEN6ZPO4V2N5IMMMN","json":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN.json","graph_json":"https://pith.science/api/pith-number/PBMFKL2RIMEN6ZPO4V2N5IMMMN/graph.json","events_json":"https://pith.science/api/pith-number/PBMFKL2RIMEN6ZPO4V2N5IMMMN/events.json","paper":"https://pith.science/paper/PBMFKL2R"},"agent_actions":{"view_html":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN","download_json":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN.json","view_paper":"https://pith.science/paper/PBMFKL2R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.4332&json=true","fetch_graph":"https://pith.science/api/pith-number/PBMFKL2RIMEN6ZPO4V2N5IMMMN/graph.json","fetch_events":"https://pith.science/api/pith-number/PBMFKL2RIMEN6ZPO4V2N5IMMMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN/action/storage_attestation","attest_author":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN/action/author_attestation","sign_citation":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN/action/citation_signature","submit_replication":"https://pith.science/pith/PBMFKL2RIMEN6ZPO4V2N5IMMMN/action/replication_record"}},"created_at":"2026-05-18T04:30:26.682550+00:00","updated_at":"2026-05-18T04:30:26.682550+00:00"}