{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QK4NHNSRHEUSKRCT5CAETW5EOR","short_pith_number":"pith:QK4NHNSR","schema_version":"1.0","canonical_sha256":"82b8d3b6513929254453e88049dba474764e1a5654b01dc36882c934ae620159","source":{"kind":"arxiv","id":"1501.07625","version":3},"attestation_state":"computed","paper":{"title":"Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Jean-Pierre Demailly (IF)","submitted_at":"2015-01-28T08:47:35Z","abstract_excerpt":"The Green-Griffiths-Lang conjecture stipulates that for every projective variety $X$ of general type over ${\\mathbb C}$, there exists a proper algebraic subvariety of $X$ containing all non constant entire curves $f:{\\mathbb C}\\to X$.  Using the formalism of directed varieties, we prove here that this assertion holds true in case $X$ satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle $T\\_X$. We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurfac"},"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":"1501.07625","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-28T08:47:35Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ee909d988c5ca49a9eb68e178e19f41f825a5b117d9c8c31b61c2d84e6e083b1","abstract_canon_sha256":"9eafa3d3b8be77e48dc12dccbbfd21333544d95074b3f5b2379c208b0e9d43f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:28.299999Z","signature_b64":"xP8IDgG9JtOB1pQDDmc30UOMCDErYj7uYXuGIYayTyGcM9ta8Efmrd1epJEp/gueaHanQ9g1uUWBDf9YzUJGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82b8d3b6513929254453e88049dba474764e1a5654b01dc36882c934ae620159","last_reissued_at":"2026-05-18T02:24:28.299282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:28.299282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of the Kobayashi conjecture on the hyperbolicity of very general hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Jean-Pierre Demailly (IF)","submitted_at":"2015-01-28T08:47:35Z","abstract_excerpt":"The Green-Griffiths-Lang conjecture stipulates that for every projective variety $X$ of general type over ${\\mathbb C}$, there exists a proper algebraic subvariety of $X$ containing all non constant entire curves $f:{\\mathbb C}\\to X$.  Using the formalism of directed varieties, we prove here that this assertion holds true in case $X$ satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle $T\\_X$. We then use this fact to confirm a long-standing conjecture of Kobayashi (1970), according to which a very general algebraic hypersurfac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07625","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":"1501.07625","created_at":"2026-05-18T02:24:28.299421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07625v3","created_at":"2026-05-18T02:24:28.299421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07625","created_at":"2026-05-18T02:24:28.299421+00:00"},{"alias_kind":"pith_short_12","alias_value":"QK4NHNSRHEUS","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QK4NHNSRHEUSKRCT","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QK4NHNSR","created_at":"2026-05-18T12:29:37.295048+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/QK4NHNSRHEUSKRCT5CAETW5EOR","json":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR.json","graph_json":"https://pith.science/api/pith-number/QK4NHNSRHEUSKRCT5CAETW5EOR/graph.json","events_json":"https://pith.science/api/pith-number/QK4NHNSRHEUSKRCT5CAETW5EOR/events.json","paper":"https://pith.science/paper/QK4NHNSR"},"agent_actions":{"view_html":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR","download_json":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR.json","view_paper":"https://pith.science/paper/QK4NHNSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07625&json=true","fetch_graph":"https://pith.science/api/pith-number/QK4NHNSRHEUSKRCT5CAETW5EOR/graph.json","fetch_events":"https://pith.science/api/pith-number/QK4NHNSRHEUSKRCT5CAETW5EOR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR/action/storage_attestation","attest_author":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR/action/author_attestation","sign_citation":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR/action/citation_signature","submit_replication":"https://pith.science/pith/QK4NHNSRHEUSKRCT5CAETW5EOR/action/replication_record"}},"created_at":"2026-05-18T02:24:28.299421+00:00","updated_at":"2026-05-18T02:24:28.299421+00:00"}