{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IEULZCECCFNN22TGS7NIL7X6RM","short_pith_number":"pith:IEULZCEC","schema_version":"1.0","canonical_sha256":"4128bc8882115add6a6697da85fefe8b27ebf2a2c0922893088f7e3b464f5040","source":{"kind":"arxiv","id":"1102.4550","version":2},"attestation_state":"computed","paper":{"title":"The gonality theorem of Noether for hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Bastianelli, Pietro De Poi, Renza Cortini","submitted_at":"2011-02-22T16:52:13Z","abstract_excerpt":"It is well known since Noether that the gonality of a smooth plane curve of degree d>3 is d-1. Given a k-dimensional complex projective variety X, the most natural extension of gonality is probably the degree of irrationality, that is the minimum degree of a dominant rational map from X to $\\mathbb{P}^k$. In this paper we are aimed at extending the assertion on plane curves to smooth hypersurfaces in $\\mathbb{P}^n$ in terms of degree of irrationality. We prove that both surfaces in $\\mathbb{P}^3$ and threefolds in $\\mathbb{P}^4$ of sufficiently large degree d have degree of irrationality d-1, "},"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":"1102.4550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-02-22T16:52:13Z","cross_cats_sorted":[],"title_canon_sha256":"95b23f8c9fabce68f2cce767f87dcd725b61e4373e81d2e41f46f831b54458c0","abstract_canon_sha256":"3a405d123d9224479788ba27dd0ca7e738ae5484d5969466c643c6389a443f25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:46.841144Z","signature_b64":"BEe6IZZYYqKV3nRYz2aCppiUyN8M1NDX+Nss4WFfbscDL2XjqMQePGoFjwTunz30vAyqIzVtcM7g4nZlthOdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4128bc8882115add6a6697da85fefe8b27ebf2a2c0922893088f7e3b464f5040","last_reissued_at":"2026-05-18T02:58:46.840234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:46.840234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The gonality theorem of Noether for hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Bastianelli, Pietro De Poi, Renza Cortini","submitted_at":"2011-02-22T16:52:13Z","abstract_excerpt":"It is well known since Noether that the gonality of a smooth plane curve of degree d>3 is d-1. Given a k-dimensional complex projective variety X, the most natural extension of gonality is probably the degree of irrationality, that is the minimum degree of a dominant rational map from X to $\\mathbb{P}^k$. In this paper we are aimed at extending the assertion on plane curves to smooth hypersurfaces in $\\mathbb{P}^n$ in terms of degree of irrationality. We prove that both surfaces in $\\mathbb{P}^3$ and threefolds in $\\mathbb{P}^4$ of sufficiently large degree d have degree of irrationality d-1, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4550","kind":"arxiv","version":2},"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":"1102.4550","created_at":"2026-05-18T02:58:46.840399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4550v2","created_at":"2026-05-18T02:58:46.840399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4550","created_at":"2026-05-18T02:58:46.840399+00:00"},{"alias_kind":"pith_short_12","alias_value":"IEULZCECCFNN","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"IEULZCECCFNN22TG","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"IEULZCEC","created_at":"2026-05-18T12:26:30.835961+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/IEULZCECCFNN22TGS7NIL7X6RM","json":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM.json","graph_json":"https://pith.science/api/pith-number/IEULZCECCFNN22TGS7NIL7X6RM/graph.json","events_json":"https://pith.science/api/pith-number/IEULZCECCFNN22TGS7NIL7X6RM/events.json","paper":"https://pith.science/paper/IEULZCEC"},"agent_actions":{"view_html":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM","download_json":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM.json","view_paper":"https://pith.science/paper/IEULZCEC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4550&json=true","fetch_graph":"https://pith.science/api/pith-number/IEULZCECCFNN22TGS7NIL7X6RM/graph.json","fetch_events":"https://pith.science/api/pith-number/IEULZCECCFNN22TGS7NIL7X6RM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM/action/storage_attestation","attest_author":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM/action/author_attestation","sign_citation":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM/action/citation_signature","submit_replication":"https://pith.science/pith/IEULZCECCFNN22TGS7NIL7X6RM/action/replication_record"}},"created_at":"2026-05-18T02:58:46.840399+00:00","updated_at":"2026-05-18T02:58:46.840399+00:00"}