{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6GX46WRUBPTJKRT5DZ34FX2CH3","short_pith_number":"pith:6GX46WRU","schema_version":"1.0","canonical_sha256":"f1afcf5a340be695467d1e77c2df423ecaf0ddcb9e9d97f9782aba3ea694530b","source":{"kind":"arxiv","id":"1409.2111","version":1},"attestation_state":"computed","paper":{"title":"Plane algebraic curves of arbitrary genus via Heegaard Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Maciej Borodzik, Matthew Hedden","submitted_at":"2014-09-07T12:10:14Z","abstract_excerpt":"Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets of knots {K_i} that can arise as the links of singularities of cuspidal curves. We combine algebro-geometric constraints with ours to solve the existence problem for curves with genus one, d>33, that possess exactly one singularity which has exactly one Puiseux pair (p;q). The realized triples (p,d,q) are expressed as successive even terms in the Fibonacci "},"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":"1409.2111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-09-07T12:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"2b1c6383191006b206127616931babea01229b6429ecacd16d282e21027c344d","abstract_canon_sha256":"d70733e5f02e571386810c2d87425f1f15982ff5776206372197f69ae66ad898"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:57.161372Z","signature_b64":"HuDkR279FtsbmKrK19jJcy/Bxx+T2b5nMk3Wddd/Z/FenlD4iaj+z42D6molFoNCSd+0rEn3ttZLcPsJ1i4LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1afcf5a340be695467d1e77c2df423ecaf0ddcb9e9d97f9782aba3ea694530b","last_reissued_at":"2026-05-18T00:39:57.160744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:57.160744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plane algebraic curves of arbitrary genus via Heegaard Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Maciej Borodzik, Matthew Hedden","submitted_at":"2014-09-07T12:10:14Z","abstract_excerpt":"Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets of knots {K_i} that can arise as the links of singularities of cuspidal curves. We combine algebro-geometric constraints with ours to solve the existence problem for curves with genus one, d>33, that possess exactly one singularity which has exactly one Puiseux pair (p;q). The realized triples (p,d,q) are expressed as successive even terms in the Fibonacci "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2111","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":"1409.2111","created_at":"2026-05-18T00:39:57.160835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.2111v1","created_at":"2026-05-18T00:39:57.160835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2111","created_at":"2026-05-18T00:39:57.160835+00:00"},{"alias_kind":"pith_short_12","alias_value":"6GX46WRUBPTJ","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6GX46WRUBPTJKRT5","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6GX46WRU","created_at":"2026-05-18T12:28:16.859392+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/6GX46WRUBPTJKRT5DZ34FX2CH3","json":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3.json","graph_json":"https://pith.science/api/pith-number/6GX46WRUBPTJKRT5DZ34FX2CH3/graph.json","events_json":"https://pith.science/api/pith-number/6GX46WRUBPTJKRT5DZ34FX2CH3/events.json","paper":"https://pith.science/paper/6GX46WRU"},"agent_actions":{"view_html":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3","download_json":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3.json","view_paper":"https://pith.science/paper/6GX46WRU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.2111&json=true","fetch_graph":"https://pith.science/api/pith-number/6GX46WRUBPTJKRT5DZ34FX2CH3/graph.json","fetch_events":"https://pith.science/api/pith-number/6GX46WRUBPTJKRT5DZ34FX2CH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3/action/storage_attestation","attest_author":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3/action/author_attestation","sign_citation":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3/action/citation_signature","submit_replication":"https://pith.science/pith/6GX46WRUBPTJKRT5DZ34FX2CH3/action/replication_record"}},"created_at":"2026-05-18T00:39:57.160835+00:00","updated_at":"2026-05-18T00:39:57.160835+00:00"}