{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:F2J3KPK32ZI3D4UUHEBECS6KF6","short_pith_number":"pith:F2J3KPK3","schema_version":"1.0","canonical_sha256":"2e93b53d5bd651b1f2943902414bca2f82323a8acd0ed898d20a958731e68680","source":{"kind":"arxiv","id":"1805.02978","version":1},"attestation_state":"computed","paper":{"title":"Bielliptic smooth plane curves and quadratic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Eslam Badr, Francesc Bars","submitted_at":"2018-05-08T12:37:01Z","abstract_excerpt":"Let $C_k$ be a smooth projective curve over a global field $k$, which is neither rational nor elliptic. Harris-Silverman, when $p=0$, and Schweizer, when $p>0$ together with an extra condition on the Jacobian variety $\\operatorname{Jac}(C_k)$ arising from Mordell's conjecture, showed that $C$ has infinitely many quadratic points over some finite field extension $L/k$ inside $\\overline{k}$ (a fixed algebraic closure of $k$) if and only if $C$ is hyperelliptic or bielliptic.\n  Now, let $C_k$ be a smooth plane curve of a fixed degree $d\\geq4$ with $p=0$ or $p>(d-1)(d-2)+1$ (up to an extra conditi"},"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":"1805.02978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-08T12:37:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5bf8166e18869c47799347202791af46fd57e984d2d8ce61050c6782d68b8390","abstract_canon_sha256":"9d3a2513da6920083527b36a7fd710bcbad2e9a8e4d0950dc997ebad05119b2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:35.039190Z","signature_b64":"8J30PwSNM2ckkrodSdWKSGK33cvKoj7tdsjLBf6KzI0ztpeCsPysKuACYNjCviFupZA98QevaAmicPgYKeMvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e93b53d5bd651b1f2943902414bca2f82323a8acd0ed898d20a958731e68680","last_reissued_at":"2026-05-18T00:16:35.038614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:35.038614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bielliptic smooth plane curves and quadratic points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Eslam Badr, Francesc Bars","submitted_at":"2018-05-08T12:37:01Z","abstract_excerpt":"Let $C_k$ be a smooth projective curve over a global field $k$, which is neither rational nor elliptic. Harris-Silverman, when $p=0$, and Schweizer, when $p>0$ together with an extra condition on the Jacobian variety $\\operatorname{Jac}(C_k)$ arising from Mordell's conjecture, showed that $C$ has infinitely many quadratic points over some finite field extension $L/k$ inside $\\overline{k}$ (a fixed algebraic closure of $k$) if and only if $C$ is hyperelliptic or bielliptic.\n  Now, let $C_k$ be a smooth plane curve of a fixed degree $d\\geq4$ with $p=0$ or $p>(d-1)(d-2)+1$ (up to an extra conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02978","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":"1805.02978","created_at":"2026-05-18T00:16:35.038706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.02978v1","created_at":"2026-05-18T00:16:35.038706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02978","created_at":"2026-05-18T00:16:35.038706+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2J3KPK32ZI3","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2J3KPK32ZI3D4UU","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2J3KPK3","created_at":"2026-05-18T12:32:22.470017+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/F2J3KPK32ZI3D4UUHEBECS6KF6","json":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6.json","graph_json":"https://pith.science/api/pith-number/F2J3KPK32ZI3D4UUHEBECS6KF6/graph.json","events_json":"https://pith.science/api/pith-number/F2J3KPK32ZI3D4UUHEBECS6KF6/events.json","paper":"https://pith.science/paper/F2J3KPK3"},"agent_actions":{"view_html":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6","download_json":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6.json","view_paper":"https://pith.science/paper/F2J3KPK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.02978&json=true","fetch_graph":"https://pith.science/api/pith-number/F2J3KPK32ZI3D4UUHEBECS6KF6/graph.json","fetch_events":"https://pith.science/api/pith-number/F2J3KPK32ZI3D4UUHEBECS6KF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6/action/storage_attestation","attest_author":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6/action/author_attestation","sign_citation":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6/action/citation_signature","submit_replication":"https://pith.science/pith/F2J3KPK32ZI3D4UUHEBECS6KF6/action/replication_record"}},"created_at":"2026-05-18T00:16:35.038706+00:00","updated_at":"2026-05-18T00:16:35.038706+00:00"}