{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4SV2CGBWNCNQB3Q5JQ6VCEVLPN","short_pith_number":"pith:4SV2CGBW","schema_version":"1.0","canonical_sha256":"e4aba11836689b00ee1d4c3d5112ab7b4be467c7b28c5494226c1c3ec2de18cb","source":{"kind":"arxiv","id":"1610.07971","version":1},"attestation_state":"computed","paper":{"title":"On rational triangles via algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farida shahata, Mohammad Sadek","submitted_at":"2016-10-25T17:18:13Z","abstract_excerpt":"A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between each family and the set of rational points of an algebraic curve. These algebraic curves are: a curve of genus 0, an elliptic curve, and a genus 3 curve. We study the set of rational points on each of these curves and describe some of its rational points explicitly."},"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":"1610.07971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T17:18:13Z","cross_cats_sorted":[],"title_canon_sha256":"bc0830d07ca50743d3c7c9ade80dbef2e44d9eab70a7c7f6c7c6ed1618b2be38","abstract_canon_sha256":"3ce35274ce8a0b820eae037f5dce3e8cdd52863563cc1ce9c690e90129b7c68f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.567565Z","signature_b64":"MqouzG6RYOTHuchpv5g3r6mDXrc4/PvYiPd0dHOhHTHedJSn6Ejv32t1QJjsB9QJ7wM2vc15nhNscU0xoBCzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4aba11836689b00ee1d4c3d5112ab7b4be467c7b28c5494226c1c3ec2de18cb","last_reissued_at":"2026-05-18T00:10:19.566914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.566914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On rational triangles via algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farida shahata, Mohammad Sadek","submitted_at":"2016-10-25T17:18:13Z","abstract_excerpt":"A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between each family and the set of rational points of an algebraic curve. These algebraic curves are: a curve of genus 0, an elliptic curve, and a genus 3 curve. We study the set of rational points on each of these curves and describe some of its rational points explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07971","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":"1610.07971","created_at":"2026-05-18T00:10:19.567017+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07971v1","created_at":"2026-05-18T00:10:19.567017+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07971","created_at":"2026-05-18T00:10:19.567017+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SV2CGBWNCNQ","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SV2CGBWNCNQB3Q5","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SV2CGBW","created_at":"2026-05-18T12:29:58.707656+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/4SV2CGBWNCNQB3Q5JQ6VCEVLPN","json":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN.json","graph_json":"https://pith.science/api/pith-number/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/graph.json","events_json":"https://pith.science/api/pith-number/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/events.json","paper":"https://pith.science/paper/4SV2CGBW"},"agent_actions":{"view_html":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN","download_json":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN.json","view_paper":"https://pith.science/paper/4SV2CGBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07971&json=true","fetch_graph":"https://pith.science/api/pith-number/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/graph.json","fetch_events":"https://pith.science/api/pith-number/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/action/storage_attestation","attest_author":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/action/author_attestation","sign_citation":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/action/citation_signature","submit_replication":"https://pith.science/pith/4SV2CGBWNCNQB3Q5JQ6VCEVLPN/action/replication_record"}},"created_at":"2026-05-18T00:10:19.567017+00:00","updated_at":"2026-05-18T00:10:19.567017+00:00"}