{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:Q4OUZX25MI7G2BQJZQFQAJ3B26","short_pith_number":"pith:Q4OUZX25","schema_version":"1.0","canonical_sha256":"871d4cdf5d623e6d0609cc0b002761d79821b931b08c6e8fd6039f37c4509ef9","source":{"kind":"arxiv","id":"alg-geom/9312008","version":1},"attestation_state":"computed","paper":{"title":"On the Hyperbolicity of the Complements of Curves in Algebraic Surfaces: The Three Component Case","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Georg Schumacher, Gerd Dethloff, Pit-Mann Wong","submitted_at":"1993-12-14T13:06:20Z","abstract_excerpt":"The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a line and three quadrics. The main results are Let C be the union of three curves in P_2 whose degrees are at least two, one of which is at least three. Then for generic such configurations the complement of C is hyperbolic and hyperbolically embedded. The same statement holds for complements of curves in generic hypersurfaces X of degree at least five and curv"},"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":"alg-geom/9312008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-12-14T13:06:20Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ff08f799172e6fa7600a028c4ec6d3e980875a4d7bfe9fee825947a8ae5554d4","abstract_canon_sha256":"247544af86b6a937e7b5282fe19b3d9f33d44b0e5f1aee9f6a126262e2266cde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:31.878831Z","signature_b64":"g6zC6Zy7jRO+tuWL3BIrhvSoP+hpP16Luzp10VYNqd/qpzbVYVYL2s1OZosz2LhE2Id2ExwBvVZ9d7aK3DtDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"871d4cdf5d623e6d0609cc0b002761d79821b931b08c6e8fd6039f37c4509ef9","last_reissued_at":"2026-05-18T02:32:31.878435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:31.878435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Hyperbolicity of the Complements of Curves in Algebraic Surfaces: The Three Component Case","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Georg Schumacher, Gerd Dethloff, Pit-Mann Wong","submitted_at":"1993-12-14T13:06:20Z","abstract_excerpt":"The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a line and three quadrics. The main results are Let C be the union of three curves in P_2 whose degrees are at least two, one of which is at least three. Then for generic such configurations the complement of C is hyperbolic and hyperbolically embedded. The same statement holds for complements of curves in generic hypersurfaces X of degree at least five and curv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9312008","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9312008","created_at":"2026-05-18T02:32:31.878495+00:00"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9312008v1","created_at":"2026-05-18T02:32:31.878495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9312008","created_at":"2026-05-18T02:32:31.878495+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4OUZX25MI7G","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4OUZX25MI7G2BQJ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4OUZX25","created_at":"2026-05-18T12:25:47.102015+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/Q4OUZX25MI7G2BQJZQFQAJ3B26","json":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26.json","graph_json":"https://pith.science/api/pith-number/Q4OUZX25MI7G2BQJZQFQAJ3B26/graph.json","events_json":"https://pith.science/api/pith-number/Q4OUZX25MI7G2BQJZQFQAJ3B26/events.json","paper":"https://pith.science/paper/Q4OUZX25"},"agent_actions":{"view_html":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26","download_json":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26.json","view_paper":"https://pith.science/paper/Q4OUZX25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=alg-geom/9312008&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4OUZX25MI7G2BQJZQFQAJ3B26/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4OUZX25MI7G2BQJZQFQAJ3B26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26/action/storage_attestation","attest_author":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26/action/author_attestation","sign_citation":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26/action/citation_signature","submit_replication":"https://pith.science/pith/Q4OUZX25MI7G2BQJZQFQAJ3B26/action/replication_record"}},"created_at":"2026-05-18T02:32:31.878495+00:00","updated_at":"2026-05-18T02:32:31.878495+00:00"}