{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7BC6KJKBVTM33AAAGLMMRP2OHG","short_pith_number":"pith:7BC6KJKB","canonical_record":{"source":{"id":"1103.5822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T04:59:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5d3a5cb3f08650ebcaa37a7c63bf77e67b05c4c935d7beb8ca2b27f1e42c6782","abstract_canon_sha256":"9b296b780c627529c207ef69005e61748816c7b7539f79d85a8660f9ce31e306"},"schema_version":"1.0"},"canonical_sha256":"f845e52541acd9bd800032d8c8bf4e398845aa0d8b9bd5c27aa8779b5009c6da","source":{"kind":"arxiv","id":"1103.5822","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5822","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5822v1","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5822","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"7BC6KJKBVTM3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7BC6KJKBVTM33AAA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7BC6KJKB","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7BC6KJKBVTM33AAAGLMMRP2OHG","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T04:59:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5d3a5cb3f08650ebcaa37a7c63bf77e67b05c4c935d7beb8ca2b27f1e42c6782","abstract_canon_sha256":"9b296b780c627529c207ef69005e61748816c7b7539f79d85a8660f9ce31e306"},"schema_version":"1.0"},"canonical_sha256":"f845e52541acd9bd800032d8c8bf4e398845aa0d8b9bd5c27aa8779b5009c6da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:27.503652Z","signature_b64":"OCEXSwqEIeWlsm06m8ka3HhODErS9dzTQGOxQbuFLZq/uLXwtYYemo/b6RY2MYvnVkpFIAy7l42RzrkD4uF1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f845e52541acd9bd800032d8c8bf4e398845aa0d8b9bd5c27aa8779b5009c6da","last_reissued_at":"2026-05-18T04:25:27.502822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:27.502822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5822","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5+9iIernmMAEB8sH5N5qopBPP1Pidh1JR5zqC5p5oHlOpQ5ItNgU10oMJuexuyVHV0V6LfDiv5uJsY5myJ+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:25:29.454156Z"},"content_sha256":"b54cd4a3d1bfbecada1a9903f157f2e8e44edb547e360c75fb2297babfda2527","schema_version":"1.0","event_id":"sha256:b54cd4a3d1bfbecada1a9903f157f2e8e44edb547e360c75fb2297babfda2527"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7BC6KJKBVTM33AAAGLMMRP2OHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order of Meromorphic Maps and Rationality of the Image Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"J\\\"org Winkelmann, Junjiro Noguchi","submitted_at":"2011-03-30T04:59:02Z","abstract_excerpt":"Let $\\iota : \\C^2 \\hookrightarrow S$ be a compactification of the two dimensional complex space $\\C^2$. By making use of Nevanlinna theoretic methods and the classification of compact complex surfaces K. Kodaira proved in 1971 (\\cite{ko71}) that $S$ is a rational surface. Here we deal with a more general meromorphic map $f: \\C^n \\to X$ into a compact complex manifold $X$ of dimension $n$, whose differential $df$ has generically rank $n$. Let $\\rho_f$ denote the order of $f$. We will prove that if $\\rho_f<2$, then every global symmetric holomorphic tensor must vanish; in particular, {\\it if $\\d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5822","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFwm/++dn4jHUw+7qwLSYvl7D4izg4TWquEiljKb/59laGi5Mi9ivUkna4FeZ9bT1cTq7vVhmyZRwQmeGChEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:25:29.454779Z"},"content_sha256":"09900f143f4b5ce06fb0285a075f6be975f03eb1f0ca3b620749515a543622e2","schema_version":"1.0","event_id":"sha256:09900f143f4b5ce06fb0285a075f6be975f03eb1f0ca3b620749515a543622e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/bundle.json","state_url":"https://pith.science/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/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":"2026-06-11T02:25:29Z","links":{"resolver":"https://pith.science/pith/7BC6KJKBVTM33AAAGLMMRP2OHG","bundle":"https://pith.science/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/bundle.json","state":"https://pith.science/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BC6KJKBVTM33AAAGLMMRP2OHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7BC6KJKBVTM33AAAGLMMRP2OHG","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":"9b296b780c627529c207ef69005e61748816c7b7539f79d85a8660f9ce31e306","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T04:59:02Z","title_canon_sha256":"5d3a5cb3f08650ebcaa37a7c63bf77e67b05c4c935d7beb8ca2b27f1e42c6782"},"schema_version":"1.0","source":{"id":"1103.5822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5822","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5822v1","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5822","created_at":"2026-05-18T04:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"7BC6KJKBVTM3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7BC6KJKBVTM33AAA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7BC6KJKB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:09900f143f4b5ce06fb0285a075f6be975f03eb1f0ca3b620749515a543622e2","target":"graph","created_at":"2026-05-18T04:25:27Z","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 $\\iota : \\C^2 \\hookrightarrow S$ be a compactification of the two dimensional complex space $\\C^2$. By making use of Nevanlinna theoretic methods and the classification of compact complex surfaces K. Kodaira proved in 1971 (\\cite{ko71}) that $S$ is a rational surface. Here we deal with a more general meromorphic map $f: \\C^n \\to X$ into a compact complex manifold $X$ of dimension $n$, whose differential $df$ has generically rank $n$. Let $\\rho_f$ denote the order of $f$. We will prove that if $\\rho_f<2$, then every global symmetric holomorphic tensor must vanish; in particular, {\\it if $\\d","authors_text":"J\\\"org Winkelmann, Junjiro Noguchi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T04:59:02Z","title":"Order of Meromorphic Maps and Rationality of the Image Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5822","kind":"arxiv","version":1},"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:b54cd4a3d1bfbecada1a9903f157f2e8e44edb547e360c75fb2297babfda2527","target":"record","created_at":"2026-05-18T04:25:27Z","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":"9b296b780c627529c207ef69005e61748816c7b7539f79d85a8660f9ce31e306","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-30T04:59:02Z","title_canon_sha256":"5d3a5cb3f08650ebcaa37a7c63bf77e67b05c4c935d7beb8ca2b27f1e42c6782"},"schema_version":"1.0","source":{"id":"1103.5822","kind":"arxiv","version":1}},"canonical_sha256":"f845e52541acd9bd800032d8c8bf4e398845aa0d8b9bd5c27aa8779b5009c6da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f845e52541acd9bd800032d8c8bf4e398845aa0d8b9bd5c27aa8779b5009c6da","first_computed_at":"2026-05-18T04:25:27.502822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:27.502822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCEXSwqEIeWlsm06m8ka3HhODErS9dzTQGOxQbuFLZq/uLXwtYYemo/b6RY2MYvnVkpFIAy7l42RzrkD4uF1CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:27.503652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b54cd4a3d1bfbecada1a9903f157f2e8e44edb547e360c75fb2297babfda2527","sha256:09900f143f4b5ce06fb0285a075f6be975f03eb1f0ca3b620749515a543622e2"],"state_sha256":"707ab63631b09ba92132ac5a22f3bd8ec59267544365923b4861c9a6342245ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PG5hCbQEi0JW+PI2G1Xrm8kpQDuBGiurW3x839IwMmalRaB47gbXBF6/R6xeOdZ1+6/AwtlDHyzRG5vdPnIxDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:25:29.458336Z","bundle_sha256":"a351a1265f8e69bd5090e2c4977dad04b9dfce2acacf6743ccc83f54f6551b4e"}}