{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:AJJPPO4VOZCBAAROVB6QZO25JV","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":"325584996906aacd7ef986670ffd44d89d253eae288fa55edcc9ce781b4993e7","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-14T15:28:02Z","title_canon_sha256":"6f25274af99f773c2fb66b510ede4275b815b8b41f7e64d22953dce1662e538f"},"schema_version":"1.0","source":{"id":"math/0103084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103084","created_at":"2026-07-04T14:35:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103084v2","created_at":"2026-07-04T14:35:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103084","created_at":"2026-07-04T14:35:07Z"},{"alias_kind":"pith_short_12","alias_value":"AJJPPO4VOZCB","created_at":"2026-07-04T14:35:07Z"},{"alias_kind":"pith_short_16","alias_value":"AJJPPO4VOZCBAARO","created_at":"2026-07-04T14:35:07Z"},{"alias_kind":"pith_short_8","alias_value":"AJJPPO4V","created_at":"2026-07-04T14:35:07Z"}],"graph_snapshots":[{"event_id":"sha256:e90b8713b0047ada735a0bbe415ebb95851427783f2b4742e46c7a042781cc37","target":"graph","created_at":"2026-07-04T14:35:07Z","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/math/0103084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We call a log variety (X, D) algebraically hyperbolic if there exists a positive number e such that 2g(C) - 2 + i(C, D) >= e deg(C) for all curves C on X, where i(C, D) is the number of the intersections between D and the normalization of C. Among other things, we proved that (P^2, D) is algebraically hyperbolic for a very general curve D of degree at least 5. More specifically, we showed that 2g(C) - 2 + i(C, D) >= (deg(D) - 4) deg C for all curves C on P^2. For example, fix a very general quintic curve D and then for any map f: C = P^1 --> P^2, there are at least deg(f) + 2 distinct points o","authors_text":"Xi Chen","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-03-14T15:28:02Z","title":"On Algebraic Hyperbolicity of Log Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103084","kind":"arxiv","version":2},"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":"sha256:501e0a8802917138464d1af286caf46e4fb7c9af1c2a957a014d19a3317a0797","target":"record","created_at":"2026-07-04T14:35:07Z","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":"325584996906aacd7ef986670ffd44d89d253eae288fa55edcc9ce781b4993e7","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-14T15:28:02Z","title_canon_sha256":"6f25274af99f773c2fb66b510ede4275b815b8b41f7e64d22953dce1662e538f"},"schema_version":"1.0","source":{"id":"math/0103084","kind":"arxiv","version":2}},"canonical_sha256":"0252f7bb95764410022ea87d0cbb5d4d41e5f5bdd9eff04962ebb9977d2bc1c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0252f7bb95764410022ea87d0cbb5d4d41e5f5bdd9eff04962ebb9977d2bc1c8","first_computed_at":"2026-07-04T14:35:07.024746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:07.024746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4U4N76+DT9xJzMuU1MCoHh5u7PMrnMdD7y4ML2br4lstvk353Xhj8vUD7Dc4iOanv3VxfTiL4bD1JpEDRuY3DA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:07.025117Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0103084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:501e0a8802917138464d1af286caf46e4fb7c9af1c2a957a014d19a3317a0797","sha256:e90b8713b0047ada735a0bbe415ebb95851427783f2b4742e46c7a042781cc37"],"state_sha256":"126e6d2250cba54a7a0332a7174f80a4698c535d3721a50201098ea8213b4e93"}