{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:QPWZIHEHWAZUGTMSRGMSWR2SQT","short_pith_number":"pith:QPWZIHEH","canonical_record":{"source":{"id":"2108.12896","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-29T19:30:07Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"74e9b8edbccfb60b68067d55193045979fe65e054ef37cb57c1a41ed1751ecad","abstract_canon_sha256":"3f09c15a77ce7c248003a6954ed787b7b0ceeee243b70a84bcad7154c59861b6"},"schema_version":"1.0"},"canonical_sha256":"83ed941c87b033434d9289992b475284deefa0be33fca4ae780e2c98580b3a9c","source":{"kind":"arxiv","id":"2108.12896","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.12896","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"2108.12896v6","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.12896","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"QPWZIHEHWAZU","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"QPWZIHEHWAZUGTMS","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"QPWZIHEH","created_at":"2026-07-05T06:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:QPWZIHEHWAZUGTMSRGMSWR2SQT","target":"record","payload":{"canonical_record":{"source":{"id":"2108.12896","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-29T19:30:07Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"74e9b8edbccfb60b68067d55193045979fe65e054ef37cb57c1a41ed1751ecad","abstract_canon_sha256":"3f09c15a77ce7c248003a6954ed787b7b0ceeee243b70a84bcad7154c59861b6"},"schema_version":"1.0"},"canonical_sha256":"83ed941c87b033434d9289992b475284deefa0be33fca4ae780e2c98580b3a9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:25:54.254153Z","signature_b64":"hHZndms8bZAhkcUWpyLWv0BU/ZY/CERq4tScFZKPg/lME2+p/ZMPhA119rrGR+VgEyWGjmhcZ1a0lG5Qak6CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83ed941c87b033434d9289992b475284deefa0be33fca4ae780e2c98580b3a9c","last_reissued_at":"2026-07-05T06:25:54.253682Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:25:54.253682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.12896","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:25:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZOJUUniijC0Pbm9NCUoZ41baOK0XW5Rou2qRqB6e93L6zsb6GhoouHvgQ6KF9wmxfmXRv9zaylCXz5uuvH+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:07:57.616697Z"},"content_sha256":"d0ec4a11ea56c77bf2ebc49a66718da6356b5849a65c21f0439e1a1a22666738","schema_version":"1.0","event_id":"sha256:d0ec4a11ea56c77bf2ebc49a66718da6356b5849a65c21f0439e1a1a22666738"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:QPWZIHEHWAZUGTMSRGMSWR2SQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological calculation of local cohomological dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Morihiko Saito, Thomas Reichelt, Uli Walther","submitted_at":"2021-08-29T19:30:07Z","abstract_excerpt":"We show that the sum of the local cohomological dimension and the rectified $\\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is then calculated using the cohomology of the links of the analytic space. In the algebraic case the first assertion is equivalent to the coincidence of the rectified $\\mathbb Q$-homological depth with the de Rham depth studied by Ogus, and follows essentially from his work. As a corollary we show that the local cohomological dimension of a quasi-proje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.12896","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.12896/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:25:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PF2O8OIY8G2ULkCeGYAIxm24nXMQUeBzWUfLtey/FsEPSPr15s2MwBbxSLZcMc23016vjM6puQq6IsaDiTkkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:07:57.617086Z"},"content_sha256":"e25a50ec66ca7b0b0a60e6692a3dcbc9bbb18557bd2faf4fb333b64f844e73e6","schema_version":"1.0","event_id":"sha256:e25a50ec66ca7b0b0a60e6692a3dcbc9bbb18557bd2faf4fb333b64f844e73e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/bundle.json","state_url":"https://pith.science/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/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":"2026-07-06T19:07:57Z","links":{"resolver":"https://pith.science/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT","bundle":"https://pith.science/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/bundle.json","state":"https://pith.science/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPWZIHEHWAZUGTMSRGMSWR2SQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QPWZIHEHWAZUGTMSRGMSWR2SQT","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":"3f09c15a77ce7c248003a6954ed787b7b0ceeee243b70a84bcad7154c59861b6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-29T19:30:07Z","title_canon_sha256":"74e9b8edbccfb60b68067d55193045979fe65e054ef37cb57c1a41ed1751ecad"},"schema_version":"1.0","source":{"id":"2108.12896","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.12896","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"2108.12896v6","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.12896","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"QPWZIHEHWAZU","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"QPWZIHEHWAZUGTMS","created_at":"2026-07-05T06:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"QPWZIHEH","created_at":"2026-07-05T06:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:e25a50ec66ca7b0b0a60e6692a3dcbc9bbb18557bd2faf4fb333b64f844e73e6","target":"graph","created_at":"2026-07-05T06:25:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.12896/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the sum of the local cohomological dimension and the rectified $\\mathbb Q$-homological depth of a closed analytic subspace of a complex manifold coincide with the dimension of the ambient manifold. The local cohomological dimension is then calculated using the cohomology of the links of the analytic space. In the algebraic case the first assertion is equivalent to the coincidence of the rectified $\\mathbb Q$-homological depth with the de Rham depth studied by Ogus, and follows essentially from his work. As a corollary we show that the local cohomological dimension of a quasi-proje","authors_text":"Morihiko Saito, Thomas Reichelt, Uli Walther","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-29T19:30:07Z","title":"Topological calculation of local cohomological dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.12896","kind":"arxiv","version":6},"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:d0ec4a11ea56c77bf2ebc49a66718da6356b5849a65c21f0439e1a1a22666738","target":"record","created_at":"2026-07-05T06:25:54Z","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":"3f09c15a77ce7c248003a6954ed787b7b0ceeee243b70a84bcad7154c59861b6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-08-29T19:30:07Z","title_canon_sha256":"74e9b8edbccfb60b68067d55193045979fe65e054ef37cb57c1a41ed1751ecad"},"schema_version":"1.0","source":{"id":"2108.12896","kind":"arxiv","version":6}},"canonical_sha256":"83ed941c87b033434d9289992b475284deefa0be33fca4ae780e2c98580b3a9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ed941c87b033434d9289992b475284deefa0be33fca4ae780e2c98580b3a9c","first_computed_at":"2026-07-05T06:25:54.253682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:25:54.253682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHZndms8bZAhkcUWpyLWv0BU/ZY/CERq4tScFZKPg/lME2+p/ZMPhA119rrGR+VgEyWGjmhcZ1a0lG5Qak6CDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:25:54.254153Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.12896","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0ec4a11ea56c77bf2ebc49a66718da6356b5849a65c21f0439e1a1a22666738","sha256:e25a50ec66ca7b0b0a60e6692a3dcbc9bbb18557bd2faf4fb333b64f844e73e6"],"state_sha256":"51cc7ff7c784d6bc47f9613952b9ba299576cd70a88a1a482607478fa8b25b18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zI4WfKRMbc9ayBjshpkfEngPgx7lHUZVdW1deD37+q2bjzvs3B/7IUZx+3aMd3bHvQBEX2iImVXW/n98oe1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:07:57.619028Z","bundle_sha256":"99ebed6444ffa61f7e277b66ba0ab4488c51c7bce6e8886c8035bcbd6bacb7f5"}}