{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:VS2JVXKLPZ3RCA5DNJUKER6DUE","short_pith_number":"pith:VS2JVXKL","schema_version":"1.0","canonical_sha256":"acb49add4b7e771103a36a68a247c3a13d9b46afe45cd740c02649eba8ed0da8","source":{"kind":"arxiv","id":"2203.01392","version":1},"attestation_state":"computed","paper":{"title":"Algebraic hyperbolicity of very general hypersurfaces in products of projective spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wern Yeong","submitted_at":"2022-03-02T20:30:59Z","abstract_excerpt":"We study the algebraic hyperbolicity of very general hypersurfaces in $\\mathbb{P}^m \\times \\mathbb{P}^n$ by using three techniques that build on past work by Ein, Voisin, Pacienza, Coskun and Riedl, and others. As a result, we completely answer the question of whether or not a very general hypersurface of bidegree $(a,b)$ in $\\mathbb{P}^m \\times \\mathbb{P}^n$ is algebraically hyperbolic, except in $\\mathbb{P}^3 \\times \\mathbb{P}^1$ for the bidegrees $(a,b)= (7,3), (6,3)$ and $(5,b)$ with $b\\geq 3.$ As another application of these techniques, we improve the known result that very general hypers"},"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":"2203.01392","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-02T20:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"8e5a7a3655c93111e05494916910c9f00f687f14d4c88c2e3f80ff7f597378bd","abstract_canon_sha256":"9bcb2702455bbc99a1825821a531b29c43b9afc2e362df9832d717de99d9ea4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:01:47.548422Z","signature_b64":"9gh2CEHx/Eq6PHcujwk8fJbKkABhuvFbYp1sU6vBv8j5TbeXH2k58gy9B2QRpsH4er0fTud24lHhtQXkinonDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acb49add4b7e771103a36a68a247c3a13d9b46afe45cd740c02649eba8ed0da8","last_reissued_at":"2026-07-05T04:01:47.548008Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:01:47.548008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic hyperbolicity of very general hypersurfaces in products of projective spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wern Yeong","submitted_at":"2022-03-02T20:30:59Z","abstract_excerpt":"We study the algebraic hyperbolicity of very general hypersurfaces in $\\mathbb{P}^m \\times \\mathbb{P}^n$ by using three techniques that build on past work by Ein, Voisin, Pacienza, Coskun and Riedl, and others. As a result, we completely answer the question of whether or not a very general hypersurface of bidegree $(a,b)$ in $\\mathbb{P}^m \\times \\mathbb{P}^n$ is algebraically hyperbolic, except in $\\mathbb{P}^3 \\times \\mathbb{P}^1$ for the bidegrees $(a,b)= (7,3), (6,3)$ and $(5,b)$ with $b\\geq 3.$ As another application of these techniques, we improve the known result that very general hypers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01392","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.01392/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2203.01392","created_at":"2026-07-05T04:01:47.548064+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.01392v1","created_at":"2026-07-05T04:01:47.548064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01392","created_at":"2026-07-05T04:01:47.548064+00:00"},{"alias_kind":"pith_short_12","alias_value":"VS2JVXKLPZ3R","created_at":"2026-07-05T04:01:47.548064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VS2JVXKLPZ3RCA5D","created_at":"2026-07-05T04:01:47.548064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VS2JVXKL","created_at":"2026-07-05T04:01:47.548064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.06365","citing_title":"Algebraic hyperbolicity of surfaces in Fano threefolds with Picard number one","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE","json":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE.json","graph_json":"https://pith.science/api/pith-number/VS2JVXKLPZ3RCA5DNJUKER6DUE/graph.json","events_json":"https://pith.science/api/pith-number/VS2JVXKLPZ3RCA5DNJUKER6DUE/events.json","paper":"https://pith.science/paper/VS2JVXKL"},"agent_actions":{"view_html":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE","download_json":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE.json","view_paper":"https://pith.science/paper/VS2JVXKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.01392&json=true","fetch_graph":"https://pith.science/api/pith-number/VS2JVXKLPZ3RCA5DNJUKER6DUE/graph.json","fetch_events":"https://pith.science/api/pith-number/VS2JVXKLPZ3RCA5DNJUKER6DUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE/action/storage_attestation","attest_author":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE/action/author_attestation","sign_citation":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE/action/citation_signature","submit_replication":"https://pith.science/pith/VS2JVXKLPZ3RCA5DNJUKER6DUE/action/replication_record"}},"created_at":"2026-07-05T04:01:47.548064+00:00","updated_at":"2026-07-05T04:01:47.548064+00:00"}