{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:RZSWPLPDZYSDNSTUZVVFPHO6PV","short_pith_number":"pith:RZSWPLPD","schema_version":"1.0","canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","source":{"kind":"arxiv","id":"0706.1031","version":3},"attestation_state":"computed","paper":{"title":"Differential Equations on Complex Projective Hypersurfaces of Low Dimension","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Simone Diverio","submitted_at":"2007-06-07T15:58:57Z","abstract_excerpt":"Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\\mathbb P^{n+1}$. In this paper we find an effective lower bound for the degree of $X$, such that every holomorphic entire curve in $X$ must satisfy an algebraic differential equation of order $k=n=\\dim X$, and also similar bounds for order $k>n$. Moreover, for every integer $n\\ge 2$, we show that there are no such algebraic differential equations of order $k<n$ for a smooth hypersurface in $\\mathbb P^{n+1}$."},"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":"0706.1031","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-06-07T15:58:57Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"f3138cb1315d6cfc4576b331df684067302947302dc7c25df2947d6b49382917","abstract_canon_sha256":"030ea1e2f7ab7dff00c6c461aded97e776683ab7f263dae7cd4a37cde9df2b86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:31.915877Z","signature_b64":"ptRiK5g6TL51GvAX6dM+W2v0N+fz02xD8jcAawPJNdAKaKes2jbFct+i9uddI2zfL2N1RvfU6nJL10CceNcUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","last_reissued_at":"2026-05-18T00:47:31.915358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:31.915358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential Equations on Complex Projective Hypersurfaces of Low Dimension","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Simone Diverio","submitted_at":"2007-06-07T15:58:57Z","abstract_excerpt":"Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\\mathbb P^{n+1}$. In this paper we find an effective lower bound for the degree of $X$, such that every holomorphic entire curve in $X$ must satisfy an algebraic differential equation of order $k=n=\\dim X$, and also similar bounds for order $k>n$. Moreover, for every integer $n\\ge 2$, we show that there are no such algebraic differential equations of order $k<n$ for a smooth hypersurface in $\\mathbb P^{n+1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1031","kind":"arxiv","version":3},"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":"0706.1031","created_at":"2026-05-18T00:47:31.915442+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.1031v3","created_at":"2026-05-18T00:47:31.915442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1031","created_at":"2026-05-18T00:47:31.915442+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZSWPLPDZYSD","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZSWPLPDZYSDNSTU","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZSWPLPD","created_at":"2026-05-18T12:25:56.245647+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/RZSWPLPDZYSDNSTUZVVFPHO6PV","json":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV.json","graph_json":"https://pith.science/api/pith-number/RZSWPLPDZYSDNSTUZVVFPHO6PV/graph.json","events_json":"https://pith.science/api/pith-number/RZSWPLPDZYSDNSTUZVVFPHO6PV/events.json","paper":"https://pith.science/paper/RZSWPLPD"},"agent_actions":{"view_html":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV","download_json":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV.json","view_paper":"https://pith.science/paper/RZSWPLPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.1031&json=true","fetch_graph":"https://pith.science/api/pith-number/RZSWPLPDZYSDNSTUZVVFPHO6PV/graph.json","fetch_events":"https://pith.science/api/pith-number/RZSWPLPDZYSDNSTUZVVFPHO6PV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/action/storage_attestation","attest_author":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/action/author_attestation","sign_citation":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/action/citation_signature","submit_replication":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/action/replication_record"}},"created_at":"2026-05-18T00:47:31.915442+00:00","updated_at":"2026-05-18T00:47:31.915442+00:00"}