{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GQKVEOG5KFUNDFM2VOE4YBZZDV","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":"af27ebc3c063a60a24cb1fd99d8ae43cb8acc46e69b2c8f414eb163ed642bf03","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-09T10:02:40Z","title_canon_sha256":"97a2efb834f401afc0643eef44bb3186e768680eaaf5ff8205aac55cc33135df"},"schema_version":"1.0","source":{"id":"1612.02960","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02960","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02960v1","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02960","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"GQKVEOG5KFUN","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GQKVEOG5KFUNDFM2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GQKVEOG5","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:174bf02ac893b7e801d560fc5a7d63db483884423913be5fda75a438d82b69ed","target":"graph","created_at":"2026-05-18T00:55:27Z","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":"For the base field of complex numbers we discuss the relationship between categories of coherent sheaves on compact Riemann surfaces and categories of coherent sheaves on weighted smooth projective curves. This is done by bringing back to life an old theorem of Bundgaard-Nielsen-Fox proving Fenchel's conjecture for fuchsian groups.","authors_text":"Helmut Lenzing","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-09T10:02:40Z","title":"Weighted projective lines and Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02960","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":"sha256:0b3c90eb384963502db92c445f8a41bc53d353d1ec2d589883734df13207efc8","target":"record","created_at":"2026-05-18T00:55:27Z","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":"af27ebc3c063a60a24cb1fd99d8ae43cb8acc46e69b2c8f414eb163ed642bf03","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-09T10:02:40Z","title_canon_sha256":"97a2efb834f401afc0643eef44bb3186e768680eaaf5ff8205aac55cc33135df"},"schema_version":"1.0","source":{"id":"1612.02960","kind":"arxiv","version":1}},"canonical_sha256":"34155238dd5168d1959aab89cc07391d6a8d69dab16c287e30553cad7ffa1170","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34155238dd5168d1959aab89cc07391d6a8d69dab16c287e30553cad7ffa1170","first_computed_at":"2026-05-18T00:55:27.888207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:27.888207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hywgkIqgDD877GvGjMYYoEZEi6bH1urLf5qYDQatZDUsSewBE9vXMqjHXJNETFELC9GnHKcdsbA3489xiMReDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:27.888902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02960","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b3c90eb384963502db92c445f8a41bc53d353d1ec2d589883734df13207efc8","sha256:174bf02ac893b7e801d560fc5a7d63db483884423913be5fda75a438d82b69ed"],"state_sha256":"3726f4535ddcb9436ca43c1212847acbf625b39df448a2ec9567474255ed3713"}