{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NWPUR52V5HMSJXYSDXODBDT3RA","short_pith_number":"pith:NWPUR52V","schema_version":"1.0","canonical_sha256":"6d9f48f755e9d924df121ddc308e7b882d56f6d25e66da4dbe250dea86ace858","source":{"kind":"arxiv","id":"2411.14188","version":1},"attestation_state":"computed","paper":{"title":"An exact way to verify whether n is a congruent number using Heegner points","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heng Chen, Rong Ma, Tuoping Du","submitted_at":"2024-11-21T14:57:21Z","abstract_excerpt":"We introduce the relationship between congruent numbers and elliptic curves, and compute the conductor of the elliptic curve $y^2 = x^3 - n^2 x$ associated with it. Furthermore, we prove that its $L$-series coefficient $a_m = 0$ when $m \\equiv 3 \\mod 4$.By using the invariants of the elliptic curve introduced above, we calculate Heegner points to quickly verify whether $n$ is a congruent number."},"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":"2411.14188","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-21T14:57:21Z","cross_cats_sorted":[],"title_canon_sha256":"7b6b0488f6f38b1dd81d2987f399cd3ffb30a8d386a64d3a0dcb98329db14f14","abstract_canon_sha256":"efcca0d65264cc22e3b801a55ff51b4fe425bcf3b971381fdcfe467515f6c137"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:42.945045Z","signature_b64":"mDxzmaTxZSDQ1n0lj2SYMjNI9ZuafaOgukYN1Kn6MSRToCEJ/S+c0riOTdJ0uWD6bvegLlZsyf1iudGzerFbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d9f48f755e9d924df121ddc308e7b882d56f6d25e66da4dbe250dea86ace858","last_reissued_at":"2026-07-05T09:38:42.944520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:42.944520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An exact way to verify whether n is a congruent number using Heegner points","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heng Chen, Rong Ma, Tuoping Du","submitted_at":"2024-11-21T14:57:21Z","abstract_excerpt":"We introduce the relationship between congruent numbers and elliptic curves, and compute the conductor of the elliptic curve $y^2 = x^3 - n^2 x$ associated with it. Furthermore, we prove that its $L$-series coefficient $a_m = 0$ when $m \\equiv 3 \\mod 4$.By using the invariants of the elliptic curve introduced above, we calculate Heegner points to quickly verify whether $n$ is a congruent number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14188/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":"2411.14188","created_at":"2026-07-05T09:38:42.944577+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.14188v1","created_at":"2026-07-05T09:38:42.944577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14188","created_at":"2026-07-05T09:38:42.944577+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWPUR52V5HMS","created_at":"2026-07-05T09:38:42.944577+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWPUR52V5HMSJXYS","created_at":"2026-07-05T09:38:42.944577+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWPUR52V","created_at":"2026-07-05T09:38:42.944577+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/NWPUR52V5HMSJXYSDXODBDT3RA","json":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA.json","graph_json":"https://pith.science/api/pith-number/NWPUR52V5HMSJXYSDXODBDT3RA/graph.json","events_json":"https://pith.science/api/pith-number/NWPUR52V5HMSJXYSDXODBDT3RA/events.json","paper":"https://pith.science/paper/NWPUR52V"},"agent_actions":{"view_html":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA","download_json":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA.json","view_paper":"https://pith.science/paper/NWPUR52V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.14188&json=true","fetch_graph":"https://pith.science/api/pith-number/NWPUR52V5HMSJXYSDXODBDT3RA/graph.json","fetch_events":"https://pith.science/api/pith-number/NWPUR52V5HMSJXYSDXODBDT3RA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA/action/storage_attestation","attest_author":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA/action/author_attestation","sign_citation":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA/action/citation_signature","submit_replication":"https://pith.science/pith/NWPUR52V5HMSJXYSDXODBDT3RA/action/replication_record"}},"created_at":"2026-07-05T09:38:42.944577+00:00","updated_at":"2026-07-05T09:38:42.944577+00:00"}