{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:RZSWPLPDZYSDNSTUZVVFPHO6PV","short_pith_number":"pith:RZSWPLPD","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"},"canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","source":{"kind":"arxiv","id":"0706.1031","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.1031","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"0706.1031v3","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1031","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"RZSWPLPDZYSD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"RZSWPLPDZYSDNSTU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"RZSWPLPD","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:RZSWPLPDZYSDNSTUZVVFPHO6PV","target":"record","payload":{"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"},"canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","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"},"source_kind":"arxiv","source_id":"0706.1031","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2N/udzl9JV4iHHXLqUD92v/q6PweEaxaD+/UdYxK+g3AhklB/YiSj/VsTDoes254b6qbWby0OMSCE3sD8ZPKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:39.689661Z"},"content_sha256":"7dd50646b1ed478f73ee86934a38e364044928435801033c01fd2e7c48a1ed47","schema_version":"1.0","event_id":"sha256:7dd50646b1ed478f73ee86934a38e364044928435801033c01fd2e7c48a1ed47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:RZSWPLPDZYSDNSTUZVVFPHO6PV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTyPXd/AAni160ApkQBaEwzR7RTzSCfrLwPNp8qMPWLcwZYnCPXTy7U6ZiSyGxtiJo6J9/BKvQbtkiuPkYCTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:31:39.690302Z"},"content_sha256":"153d6beb9686a9118ded9e8f95970d2fc55415e7dbafce15e1bb7d89e3a4b6a4","schema_version":"1.0","event_id":"sha256:153d6beb9686a9118ded9e8f95970d2fc55415e7dbafce15e1bb7d89e3a4b6a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/bundle.json","state_url":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T14:31:39Z","links":{"resolver":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV","bundle":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/bundle.json","state":"https://pith.science/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZSWPLPDZYSDNSTUZVVFPHO6PV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:RZSWPLPDZYSDNSTUZVVFPHO6PV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"030ea1e2f7ab7dff00c6c461aded97e776683ab7f263dae7cd4a37cde9df2b86","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-07T15:58:57Z","title_canon_sha256":"f3138cb1315d6cfc4576b331df684067302947302dc7c25df2947d6b49382917"},"schema_version":"1.0","source":{"id":"0706.1031","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.1031","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"0706.1031v3","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.1031","created_at":"2026-05-18T00:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"RZSWPLPDZYSD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"RZSWPLPDZYSDNSTU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"RZSWPLPD","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:153d6beb9686a9118ded9e8f95970d2fc55415e7dbafce15e1bb7d89e3a4b6a4","target":"graph","created_at":"2026-05-18T00:47:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\mathbb P^{n+1}$.","authors_text":"Simone Diverio","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-06-07T15:58:57Z","title":"Differential Equations on Complex Projective Hypersurfaces of Low Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.1031","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7dd50646b1ed478f73ee86934a38e364044928435801033c01fd2e7c48a1ed47","target":"record","created_at":"2026-05-18T00:47:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"030ea1e2f7ab7dff00c6c461aded97e776683ab7f263dae7cd4a37cde9df2b86","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-07T15:58:57Z","title_canon_sha256":"f3138cb1315d6cfc4576b331df684067302947302dc7c25df2947d6b49382917"},"schema_version":"1.0","source":{"id":"0706.1031","kind":"arxiv","version":3}},"canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6567ade3ce2436ca74cd6a579dde7d418fa200f96531835f2b5b12ff217e43","first_computed_at":"2026-05-18T00:47:31.915358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:31.915358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptRiK5g6TL51GvAX6dM+W2v0N+fz02xD8jcAawPJNdAKaKes2jbFct+i9uddI2zfL2N1RvfU6nJL10CceNcUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:31.915877Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.1031","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7dd50646b1ed478f73ee86934a38e364044928435801033c01fd2e7c48a1ed47","sha256:153d6beb9686a9118ded9e8f95970d2fc55415e7dbafce15e1bb7d89e3a4b6a4"],"state_sha256":"2be9d1226b6c6ca7922ee9c44fed036cd40f2d388b118b6b53bdf225e0bfd767"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"22pHa7DzZ8mwSpXEIzO1fSZwFpseJUie1b7MKCD7l91TpTeA++sQaek1UGAc1yIQn21/OnLNJroCw9EKzbtTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:31:39.693878Z","bundle_sha256":"1bd29c582c681c7294bec95e80ab62b2d104a2a7d39943ad24aae581ac05a995"}}