{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7GOQT7NRMLLJH2OP5WSHIBCI6Q","short_pith_number":"pith:7GOQT7NR","canonical_record":{"source":{"id":"1101.2216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T21:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"a1e8351f75f9b172793baa00580274e985ec29c9de0483c0649e8b636e48531b","abstract_canon_sha256":"34d14a39effbafcc025aeb2a5f175b7c5b44bc7bd7af2c412d28ddfe4f6507c4"},"schema_version":"1.0"},"canonical_sha256":"f99d09fdb162d693e9cfeda4740448f400d22c76c52de0fa475aea4b35ec8345","source":{"kind":"arxiv","id":"1101.2216","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2216","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2216v1","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2216","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"7GOQT7NRMLLJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7GOQT7NRMLLJH2OP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7GOQT7NR","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7GOQT7NRMLLJH2OP5WSHIBCI6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T21:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"a1e8351f75f9b172793baa00580274e985ec29c9de0483c0649e8b636e48531b","abstract_canon_sha256":"34d14a39effbafcc025aeb2a5f175b7c5b44bc7bd7af2c412d28ddfe4f6507c4"},"schema_version":"1.0"},"canonical_sha256":"f99d09fdb162d693e9cfeda4740448f400d22c76c52de0fa475aea4b35ec8345","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:08.391703Z","signature_b64":"ab9ObQbwYK8UG7DLfDVtxEV0qpxbR7LcdotrdE2SA2nIXSnesNbnx8JgxZTfR2Nj1Imo8ujxRwHcFcVhHmJVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f99d09fdb162d693e9cfeda4740448f400d22c76c52de0fa475aea4b35ec8345","last_reissued_at":"2026-05-18T02:27:08.390957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:08.390957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2216","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWwuWUWyJZ/Jj39gOnA8cII9Jjw3c4/YTkaKhu1J7VmEZuEPiM6LA0RyH7shAyeepBax+wdJA3ZxSf/el0DCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:29:38.654387Z"},"content_sha256":"de59fc9c75f9b5a191b6cf31db90890f359f179df707650b8be85cacf9b5217a","schema_version":"1.0","event_id":"sha256:de59fc9c75f9b5a191b6cf31db90890f359f179df707650b8be85cacf9b5217a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7GOQT7NRMLLJH2OP5WSHIBCI6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Meromorphic Line Bundles and Holomorphic Gerbes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Oren Ben-Bassat","submitted_at":"2011-01-11T21:34:03Z","abstract_excerpt":"We show that any complex manifold that has a divisor whose normalization has non-zero first Betti number either has a non-trivial holomorphic gerbe which does not trivialize meromorphicly or a meromorphic line bundle not equivalent to any holomorphic line bundle. Similarly, higher Betti numbers of divisors correspond to higher gerbes or meromorphic gerbes. We give several new examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2216","kind":"arxiv","version":1},"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":"2026-05-18T02:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CnsCveOQOH0nIryzLPekzkmaVrev8PbpoDmzz6hLuOYfZ0Tcu5ZEce//8CzwczUg//WjyVb1tx7maKHkxKhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:29:38.654732Z"},"content_sha256":"d588d492fece41acc988219c2c41b53e8f187d7332133974cea53fa6ee705e64","schema_version":"1.0","event_id":"sha256:d588d492fece41acc988219c2c41b53e8f187d7332133974cea53fa6ee705e64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/bundle.json","state_url":"https://pith.science/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/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":"2026-05-30T14:29:38Z","links":{"resolver":"https://pith.science/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q","bundle":"https://pith.science/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/bundle.json","state":"https://pith.science/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7GOQT7NRMLLJH2OP5WSHIBCI6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7GOQT7NRMLLJH2OP5WSHIBCI6Q","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":"34d14a39effbafcc025aeb2a5f175b7c5b44bc7bd7af2c412d28ddfe4f6507c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T21:34:03Z","title_canon_sha256":"a1e8351f75f9b172793baa00580274e985ec29c9de0483c0649e8b636e48531b"},"schema_version":"1.0","source":{"id":"1101.2216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2216","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2216v1","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2216","created_at":"2026-05-18T02:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"7GOQT7NRMLLJ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7GOQT7NRMLLJH2OP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7GOQT7NR","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:d588d492fece41acc988219c2c41b53e8f187d7332133974cea53fa6ee705e64","target":"graph","created_at":"2026-05-18T02:27:08Z","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":"We show that any complex manifold that has a divisor whose normalization has non-zero first Betti number either has a non-trivial holomorphic gerbe which does not trivialize meromorphicly or a meromorphic line bundle not equivalent to any holomorphic line bundle. Similarly, higher Betti numbers of divisors correspond to higher gerbes or meromorphic gerbes. We give several new examples.","authors_text":"Edoardo Ballico, Oren Ben-Bassat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T21:34:03Z","title":"Meromorphic Line Bundles and Holomorphic Gerbes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2216","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:de59fc9c75f9b5a191b6cf31db90890f359f179df707650b8be85cacf9b5217a","target":"record","created_at":"2026-05-18T02:27:08Z","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":"34d14a39effbafcc025aeb2a5f175b7c5b44bc7bd7af2c412d28ddfe4f6507c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T21:34:03Z","title_canon_sha256":"a1e8351f75f9b172793baa00580274e985ec29c9de0483c0649e8b636e48531b"},"schema_version":"1.0","source":{"id":"1101.2216","kind":"arxiv","version":1}},"canonical_sha256":"f99d09fdb162d693e9cfeda4740448f400d22c76c52de0fa475aea4b35ec8345","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f99d09fdb162d693e9cfeda4740448f400d22c76c52de0fa475aea4b35ec8345","first_computed_at":"2026-05-18T02:27:08.390957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:08.390957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ab9ObQbwYK8UG7DLfDVtxEV0qpxbR7LcdotrdE2SA2nIXSnesNbnx8JgxZTfR2Nj1Imo8ujxRwHcFcVhHmJVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:08.391703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de59fc9c75f9b5a191b6cf31db90890f359f179df707650b8be85cacf9b5217a","sha256:d588d492fece41acc988219c2c41b53e8f187d7332133974cea53fa6ee705e64"],"state_sha256":"e280b5afff9df6100d522f9aa25b390468db5446d4345bf4cb4f32651c0e674a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QH9W49mHeeRHj5qMJRUhMtQPSoYD9GCTFAT7GKv4asJnQ3kta8f3aNIP0wQGMA5I6zPQFt+qlU7FlPfMpOdOBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:29:38.656634Z","bundle_sha256":"f42fe7cc896ab5e84b14a1b2d8799b23b27c0c34f4266bfaf7eb6e61b3159b56"}}