{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TGH3GZM4KFYH2S6FBYA3Z4ZC4X","short_pith_number":"pith:TGH3GZM4","canonical_record":{"source":{"id":"1411.2830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-11T14:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"2f783d12bdc7277e241ea64849bbb2d565789935059fb9e27e3da27d5bbf2c69","abstract_canon_sha256":"8c1917d33a3cde117b31699155362a8bff70516eb9a3c29ef48ec0ae7f550d88"},"schema_version":"1.0"},"canonical_sha256":"998fb3659c51707d4bc50e01bcf322e5ef56cb1826c7235678364850c54b2ab7","source":{"kind":"arxiv","id":"1411.2830","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2830","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2830v2","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2830","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"TGH3GZM4KFYH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TGH3GZM4KFYH2S6F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TGH3GZM4","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TGH3GZM4KFYH2S6FBYA3Z4ZC4X","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-11T14:34:02Z","cross_cats_sorted":[],"title_canon_sha256":"2f783d12bdc7277e241ea64849bbb2d565789935059fb9e27e3da27d5bbf2c69","abstract_canon_sha256":"8c1917d33a3cde117b31699155362a8bff70516eb9a3c29ef48ec0ae7f550d88"},"schema_version":"1.0"},"canonical_sha256":"998fb3659c51707d4bc50e01bcf322e5ef56cb1826c7235678364850c54b2ab7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:32.323213Z","signature_b64":"fV0wZ1TPnowZrfmGVRIHHTizNaBghqLHbEgmO+dnre53hU2kMKrcIrWuBqUjjro8BCi4Td4M+utRB473mUweDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"998fb3659c51707d4bc50e01bcf322e5ef56cb1826c7235678364850c54b2ab7","last_reissued_at":"2026-05-18T01:09:32.322806Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:32.322806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2830","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNyFBP4YaSdzW8Qr/2MNXaskr7pKoGtwv1naGYsni/QjE2Y2Moxw3FZKtyoQk6VffolYSrpbrUzhrcURZhzrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:44:59.896081Z"},"content_sha256":"f1e1177b926d4d7e69132e784846bc7099ef4206183684be4c3104ae3d4c3b52","schema_version":"1.0","event_id":"sha256:f1e1177b926d4d7e69132e784846bc7099ef4206183684be4c3104ae3d4c3b52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TGH3GZM4KFYH2S6FBYA3Z4ZC4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of Takegoshi's relative vanishing theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Martin Sera","submitted_at":"2014-11-11T14:34:02Z","abstract_excerpt":"We present a generalization of Takegoshi's relative version of the Grauert-Riemenschneider vanishing theorem. Under some natural assumptions, we extend Takegoshi's vanishing theorem to the case of Nakano semi-positive coherent analytic sheaves on singular complex spaces. We also obtain some new results about proper modifications of torsion-free coherent analytic sheaves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2830","kind":"arxiv","version":2},"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":"2026-05-18T01:09:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuA2QuQddimssvnltTGV+frKg3K9KbIDauC6Lad5/HPpyQKpn3uw4HyNtYM46PpBN/tQl0c2VDTbLAqBKMdLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:44:59.896437Z"},"content_sha256":"3ddd4f38766782d0df6b8e84149783780208c15995a5d7d8e0d73e9940013664","schema_version":"1.0","event_id":"sha256:3ddd4f38766782d0df6b8e84149783780208c15995a5d7d8e0d73e9940013664"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/bundle.json","state_url":"https://pith.science/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/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":"2026-06-22T23:44:59Z","links":{"resolver":"https://pith.science/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X","bundle":"https://pith.science/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/bundle.json","state":"https://pith.science/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGH3GZM4KFYH2S6FBYA3Z4ZC4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TGH3GZM4KFYH2S6FBYA3Z4ZC4X","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":"8c1917d33a3cde117b31699155362a8bff70516eb9a3c29ef48ec0ae7f550d88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-11T14:34:02Z","title_canon_sha256":"2f783d12bdc7277e241ea64849bbb2d565789935059fb9e27e3da27d5bbf2c69"},"schema_version":"1.0","source":{"id":"1411.2830","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2830","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2830v2","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2830","created_at":"2026-05-18T01:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"TGH3GZM4KFYH","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TGH3GZM4KFYH2S6F","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TGH3GZM4","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:3ddd4f38766782d0df6b8e84149783780208c15995a5d7d8e0d73e9940013664","target":"graph","created_at":"2026-05-18T01:09:32Z","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 present a generalization of Takegoshi's relative version of the Grauert-Riemenschneider vanishing theorem. Under some natural assumptions, we extend Takegoshi's vanishing theorem to the case of Nakano semi-positive coherent analytic sheaves on singular complex spaces. We also obtain some new results about proper modifications of torsion-free coherent analytic sheaves.","authors_text":"Martin Sera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-11T14:34:02Z","title":"A generalization of Takegoshi's relative vanishing theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2830","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:f1e1177b926d4d7e69132e784846bc7099ef4206183684be4c3104ae3d4c3b52","target":"record","created_at":"2026-05-18T01:09:32Z","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":"8c1917d33a3cde117b31699155362a8bff70516eb9a3c29ef48ec0ae7f550d88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-11T14:34:02Z","title_canon_sha256":"2f783d12bdc7277e241ea64849bbb2d565789935059fb9e27e3da27d5bbf2c69"},"schema_version":"1.0","source":{"id":"1411.2830","kind":"arxiv","version":2}},"canonical_sha256":"998fb3659c51707d4bc50e01bcf322e5ef56cb1826c7235678364850c54b2ab7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998fb3659c51707d4bc50e01bcf322e5ef56cb1826c7235678364850c54b2ab7","first_computed_at":"2026-05-18T01:09:32.322806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:32.322806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fV0wZ1TPnowZrfmGVRIHHTizNaBghqLHbEgmO+dnre53hU2kMKrcIrWuBqUjjro8BCi4Td4M+utRB473mUweDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:32.323213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2830","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1e1177b926d4d7e69132e784846bc7099ef4206183684be4c3104ae3d4c3b52","sha256:3ddd4f38766782d0df6b8e84149783780208c15995a5d7d8e0d73e9940013664"],"state_sha256":"395e5c6fb629130aa60c5250f207615ec3980696723a1432de2a0169b08a6136"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XU8CknF6cdGXH7QjXxlJq3lBKZgTS6H2McSy/XTDIamjr+4ouFJSxaUA7qSdV3Px35TF4ZM3kUVuetr02yG3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:44:59.898308Z","bundle_sha256":"9662ba21625fcb4313f0b2a27ec60d1d49dd2f4e259148e54f3b0863d492e553"}}