{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:3MG7X7S7HU7IHFQBA5BPU6IBZK","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":"cf6fd887039ba99ab152d388274c9e399f07f8aa2f55aad0ad9f7417ad07a667","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2002-12-28T17:32:35Z","title_canon_sha256":"aeff0b8855b8942861361a37e44922b3bbcdcdd60ff12c4f57652eb068556c62"},"schema_version":"1.0","source":{"id":"math/0212362","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0212362","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0212362v3","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0212362","created_at":"2026-05-18T03:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"3MG7X7S7HU7I","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"3MG7X7S7HU7IHFQB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"3MG7X7S7","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:945a1371937b71e56892a4091d37ebd7a48eb1eeeed08a1965eda9081867ca03","target":"graph","created_at":"2026-05-18T03:49:33Z","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"},"paper":{"abstract_excerpt":"This note contains a new proof of a theorem of Gang Xiao saying that the bicanonical map of a surface S of general type is generically finite if and only if the second plurigenus of S is strictly larger than 2. Such properties are also studied for adjoint linear systems |K_S+L|, where L is any divisor with at least 2 linearly independent sections.","authors_text":"Eckart Viehweg, Meng Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2002-12-28T17:32:35Z","title":"Bicanonical and adjoint linear systems on surfaces of general type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212362","kind":"arxiv","version":3},"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:c0df0a67c6e4822f6ffca2ba92f0f5fa99e9f62b9e654edd1b0fac14d297b07e","target":"record","created_at":"2026-05-18T03:49:33Z","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":"cf6fd887039ba99ab152d388274c9e399f07f8aa2f55aad0ad9f7417ad07a667","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2002-12-28T17:32:35Z","title_canon_sha256":"aeff0b8855b8942861361a37e44922b3bbcdcdd60ff12c4f57652eb068556c62"},"schema_version":"1.0","source":{"id":"math/0212362","kind":"arxiv","version":3}},"canonical_sha256":"db0dfbfe5f3d3e8396010742fa7901caa5c148c1a247ecffce0b1e42c7ef5708","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db0dfbfe5f3d3e8396010742fa7901caa5c148c1a247ecffce0b1e42c7ef5708","first_computed_at":"2026-05-18T03:49:33.189770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:33.189770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wp5T7FIizcnNYt8C3Fo/Y2OkHvMIerxU/bN4+gh57n5dRi1jmnqhjfruXL79c2yOOioK1KNLP+KcDImiTPOzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:33.190650Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0212362","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0df0a67c6e4822f6ffca2ba92f0f5fa99e9f62b9e654edd1b0fac14d297b07e","sha256:945a1371937b71e56892a4091d37ebd7a48eb1eeeed08a1965eda9081867ca03"],"state_sha256":"cbe44d8f05c164d37d87820832956bd403bc103c21ce0e1cea3a0cef826d1767"}