{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:GHVNWHHW23FD2VYXNHHAULI2NM","short_pith_number":"pith:GHVNWHHW","canonical_record":{"source":{"id":"0911.4473","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-11-23T19:48:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b4621ddcca75a8cfde32434001daabab5a5d8f00cde3e4589dab0c6c50662a38","abstract_canon_sha256":"51f8e480723aa170fcc364a7241aeff3b15bb7ca56f1482be499e0bdb8e96692"},"schema_version":"1.0"},"canonical_sha256":"31eadb1cf6d6ca3d571769ce0a2d1a6b21b82ed213fdb22ab425fdab9cc54c5c","source":{"kind":"arxiv","id":"0911.4473","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4473","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4473v3","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4473","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"GHVNWHHW23FD","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GHVNWHHW23FD2VYX","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GHVNWHHW","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:GHVNWHHW23FD2VYXNHHAULI2NM","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4473","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-11-23T19:48:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b4621ddcca75a8cfde32434001daabab5a5d8f00cde3e4589dab0c6c50662a38","abstract_canon_sha256":"51f8e480723aa170fcc364a7241aeff3b15bb7ca56f1482be499e0bdb8e96692"},"schema_version":"1.0"},"canonical_sha256":"31eadb1cf6d6ca3d571769ce0a2d1a6b21b82ed213fdb22ab425fdab9cc54c5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:45.284735Z","signature_b64":"r0xOs/iFK/LdXKt73t3Po8yMbgF5bVQYoSIe2KpLlDVH7tGudBGBKONCeoP/F+TKqYI0WjICUtJHnr0BkwExBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31eadb1cf6d6ca3d571769ce0a2d1a6b21b82ed213fdb22ab425fdab9cc54c5c","last_reissued_at":"2026-05-18T04:40:45.284283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:45.284283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4473","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Atr61dmyR+YtlBv9uxlXVMUhkI+ntI4JojPEi+hNz6sSJyLAm7FzTOis6IYcYHnZzduIB3gsBLwrzdheuPy8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:21:13.021279Z"},"content_sha256":"7c183b9cf8e3494a41929293146ace377d4230c0104128cb90c3f2129bca958f","schema_version":"1.0","event_id":"sha256:7c183b9cf8e3494a41929293146ace377d4230c0104128cb90c3f2129bca958f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:GHVNWHHW23FD2VYXNHHAULI2NM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introduction to coherent sheaves on weighted projective lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Henning Krause, Xiao-Wu Chen","submitted_at":"2009-11-23T19:48:51Z","abstract_excerpt":"These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a description in terms of expansions of abelian categories.\n  A weighted projective line is obtained from a projective line by inserting finitely many weights. So we describe the category of coherent sheaves on a projective line in some detail, and the insertion of weights amounts to adding simple objects. We call this process `expansion' and treat it axiomatically. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4473","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:40:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGBYOxTaSCv+BKYalvokj7o3YBPfjB884ikiH0MryyQbh7GqC984B1U0QvUFPJEPQI87hZJjEBEmkJzP2z+kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:21:13.021757Z"},"content_sha256":"24a68f2897da606faaa66d1cce7488be55c7df6e798f0d7cdf1ef692448ed0bd","schema_version":"1.0","event_id":"sha256:24a68f2897da606faaa66d1cce7488be55c7df6e798f0d7cdf1ef692448ed0bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHVNWHHW23FD2VYXNHHAULI2NM/bundle.json","state_url":"https://pith.science/pith/GHVNWHHW23FD2VYXNHHAULI2NM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHVNWHHW23FD2VYXNHHAULI2NM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T22:21:13Z","links":{"resolver":"https://pith.science/pith/GHVNWHHW23FD2VYXNHHAULI2NM","bundle":"https://pith.science/pith/GHVNWHHW23FD2VYXNHHAULI2NM/bundle.json","state":"https://pith.science/pith/GHVNWHHW23FD2VYXNHHAULI2NM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHVNWHHW23FD2VYXNHHAULI2NM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GHVNWHHW23FD2VYXNHHAULI2NM","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":"51f8e480723aa170fcc364a7241aeff3b15bb7ca56f1482be499e0bdb8e96692","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-11-23T19:48:51Z","title_canon_sha256":"b4621ddcca75a8cfde32434001daabab5a5d8f00cde3e4589dab0c6c50662a38"},"schema_version":"1.0","source":{"id":"0911.4473","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4473","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4473v3","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4473","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"GHVNWHHW23FD","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GHVNWHHW23FD2VYX","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GHVNWHHW","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:24a68f2897da606faaa66d1cce7488be55c7df6e798f0d7cdf1ef692448ed0bd","target":"graph","created_at":"2026-05-18T04:40:45Z","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":"These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a description in terms of expansions of abelian categories.\n  A weighted projective line is obtained from a projective line by inserting finitely many weights. So we describe the category of coherent sheaves on a projective line in some detail, and the insertion of weights amounts to adding simple objects. We call this process `expansion' and treat it axiomatically. Th","authors_text":"Henning Krause, Xiao-Wu Chen","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-11-23T19:48:51Z","title":"Introduction to coherent sheaves on weighted projective lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4473","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":"sha256:7c183b9cf8e3494a41929293146ace377d4230c0104128cb90c3f2129bca958f","target":"record","created_at":"2026-05-18T04:40:45Z","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":"51f8e480723aa170fcc364a7241aeff3b15bb7ca56f1482be499e0bdb8e96692","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-11-23T19:48:51Z","title_canon_sha256":"b4621ddcca75a8cfde32434001daabab5a5d8f00cde3e4589dab0c6c50662a38"},"schema_version":"1.0","source":{"id":"0911.4473","kind":"arxiv","version":3}},"canonical_sha256":"31eadb1cf6d6ca3d571769ce0a2d1a6b21b82ed213fdb22ab425fdab9cc54c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31eadb1cf6d6ca3d571769ce0a2d1a6b21b82ed213fdb22ab425fdab9cc54c5c","first_computed_at":"2026-05-18T04:40:45.284283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:45.284283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r0xOs/iFK/LdXKt73t3Po8yMbgF5bVQYoSIe2KpLlDVH7tGudBGBKONCeoP/F+TKqYI0WjICUtJHnr0BkwExBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:45.284735Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4473","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c183b9cf8e3494a41929293146ace377d4230c0104128cb90c3f2129bca958f","sha256:24a68f2897da606faaa66d1cce7488be55c7df6e798f0d7cdf1ef692448ed0bd"],"state_sha256":"d14cd60140ab04346b0c70281682b519f0a964d00409a022c83e3a2759a8ab11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vhbqj0O+s2S9P0U/iPyHtrO5wo0/C7e82A8w5c2inI4hkHdBqyReRePD4lpqDcJZoAEUyYDUfHV+iTtCRdGrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:21:13.027372Z","bundle_sha256":"871407d8cbab45e74abbc38a31a2755aa5d59f904bf407bc0bb7faa7c7513353"}}