{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VS2JVXKLPZ3RCA5DNJUKER6DUE","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":"9bcb2702455bbc99a1825821a531b29c43b9afc2e362df9832d717de99d9ea4d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-02T20:30:59Z","title_canon_sha256":"8e5a7a3655c93111e05494916910c9f00f687f14d4c88c2e3f80ff7f597378bd"},"schema_version":"1.0","source":{"id":"2203.01392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.01392","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"2203.01392v1","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01392","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"VS2JVXKLPZ3R","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_16","alias_value":"VS2JVXKLPZ3RCA5D","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_8","alias_value":"VS2JVXKL","created_at":"2026-07-05T04:01:47Z"}],"graph_snapshots":[{"event_id":"sha256:a5671e0bd13d117f2bb9a739f6f2d01aaa2ebe1b8c6565d1cb6151db1d33e48c","target":"graph","created_at":"2026-07-05T04:01:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.01392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Wern Yeong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-02T20:30:59Z","title":"Algebraic hyperbolicity of very general hypersurfaces in products of projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01392","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":"sha256:5ee9fdf599a530a217df4ffc8efc3db5736bbdb1d41dd9928d7a21ba3426d4b7","target":"record","created_at":"2026-07-05T04:01:47Z","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":"9bcb2702455bbc99a1825821a531b29c43b9afc2e362df9832d717de99d9ea4d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-02T20:30:59Z","title_canon_sha256":"8e5a7a3655c93111e05494916910c9f00f687f14d4c88c2e3f80ff7f597378bd"},"schema_version":"1.0","source":{"id":"2203.01392","kind":"arxiv","version":1}},"canonical_sha256":"acb49add4b7e771103a36a68a247c3a13d9b46afe45cd740c02649eba8ed0da8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acb49add4b7e771103a36a68a247c3a13d9b46afe45cd740c02649eba8ed0da8","first_computed_at":"2026-07-05T04:01:47.548008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:01:47.548008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9gh2CEHx/Eq6PHcujwk8fJbKkABhuvFbYp1sU6vBv8j5TbeXH2k58gy9B2QRpsH4er0fTud24lHhtQXkinonDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:01:47.548422Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.01392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee9fdf599a530a217df4ffc8efc3db5736bbdb1d41dd9928d7a21ba3426d4b7","sha256:a5671e0bd13d117f2bb9a739f6f2d01aaa2ebe1b8c6565d1cb6151db1d33e48c"],"state_sha256":"884dce80e0f108151a7f021baf572e942c5c403ed3e6d22b31657359cf26f537"}