{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GATNBMLG43CQSF6RPS3BMCMAPL","short_pith_number":"pith:GATNBMLG","canonical_record":{"source":{"id":"1903.04710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-12T03:25:42Z","cross_cats_sorted":["math.AG","math.DG","math.FA"],"title_canon_sha256":"76e43af420420911894a9f57e1a6221246105d12de48c1852d5d8fb66e80b57c","abstract_canon_sha256":"7b8427473222168394ac35f2a9b4a6035660090539ca146d423d769c69b10fa4"},"schema_version":"1.0"},"canonical_sha256":"3026d0b166e6c50917d17cb61609807ac0f76fba5f85cad2270deb743687f549","source":{"kind":"arxiv","id":"1903.04710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04710","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04710v1","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04710","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"GATNBMLG43CQ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GATNBMLG43CQSF6R","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GATNBMLG","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GATNBMLG43CQSF6RPS3BMCMAPL","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-12T03:25:42Z","cross_cats_sorted":["math.AG","math.DG","math.FA"],"title_canon_sha256":"76e43af420420911894a9f57e1a6221246105d12de48c1852d5d8fb66e80b57c","abstract_canon_sha256":"7b8427473222168394ac35f2a9b4a6035660090539ca146d423d769c69b10fa4"},"schema_version":"1.0"},"canonical_sha256":"3026d0b166e6c50917d17cb61609807ac0f76fba5f85cad2270deb743687f549","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:28.889338Z","signature_b64":"e+d5p7zMJMriPvD+FxR5iwSE3V8bGm+biiX+wiXt5KHq7jQJzS38FjHSLHVqtkTdmNlgJE8quTBsvKZEneh9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3026d0b166e6c50917d17cb61609807ac0f76fba5f85cad2270deb743687f549","last_reissued_at":"2026-05-17T23:51:28.888742Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:28.888742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04710","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":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2YpaRae1xkoJKw7RdJKWuWqN3Liva09HBHNCTVbAwRB3ILXM3Tnw9iVj2piSVwg/tlBpTs4bzTyw+rJ07KHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:00.456784Z"},"content_sha256":"6514f78b79769f3805acd2a2bd818fb45f4885a536fd444d9c1d5419ca3f9d97","schema_version":"1.0","event_id":"sha256:6514f78b79769f3805acd2a2bd818fb45f4885a536fd444d9c1d5419ca3f9d97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GATNBMLG43CQSF6RPS3BMCMAPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative Dolbeault cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG","math.FA"],"primary_cat":"math.CV","authors_text":"Tatsuo Suwa","submitted_at":"2019-03-12T03:25:42Z","abstract_excerpt":"We review the notion of relative Dolbeault cohomology and prove that it is canonically isomorphic with the local (relative) cohomology of A. Grothendieck and M. Sato with coefficients in the sheaf of holomorphic forms. We deal with this cohomology from two viewpoints. One is the Cech theoretical approach, which is convenient to define such operations as the cup product and integration and leads to the study of local duality. Along the way we also establish some notable canonical isomorphisms among various cohomologies. The other is to regard it as the cohomology of a certain complex, which is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04710","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":"2026-05-17T23:51:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vz50iUlUuLy2lQ9GeTqhiQE/fy+xMW9PBbW2/aOzU9d52kal0VWmAYCojrbYV+P4YRhm/qNlK9MMK8V9vcliAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:00.457449Z"},"content_sha256":"f5246f4c5ea78dac38aaeb83c598266319e453d7cbac387ee0ec076f5d131708","schema_version":"1.0","event_id":"sha256:f5246f4c5ea78dac38aaeb83c598266319e453d7cbac387ee0ec076f5d131708"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GATNBMLG43CQSF6RPS3BMCMAPL/bundle.json","state_url":"https://pith.science/pith/GATNBMLG43CQSF6RPS3BMCMAPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GATNBMLG43CQSF6RPS3BMCMAPL/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":"2026-05-31T10:18:00Z","links":{"resolver":"https://pith.science/pith/GATNBMLG43CQSF6RPS3BMCMAPL","bundle":"https://pith.science/pith/GATNBMLG43CQSF6RPS3BMCMAPL/bundle.json","state":"https://pith.science/pith/GATNBMLG43CQSF6RPS3BMCMAPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GATNBMLG43CQSF6RPS3BMCMAPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GATNBMLG43CQSF6RPS3BMCMAPL","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":"7b8427473222168394ac35f2a9b4a6035660090539ca146d423d769c69b10fa4","cross_cats_sorted":["math.AG","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-12T03:25:42Z","title_canon_sha256":"76e43af420420911894a9f57e1a6221246105d12de48c1852d5d8fb66e80b57c"},"schema_version":"1.0","source":{"id":"1903.04710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04710","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04710v1","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04710","created_at":"2026-05-17T23:51:28Z"},{"alias_kind":"pith_short_12","alias_value":"GATNBMLG43CQ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GATNBMLG43CQSF6R","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GATNBMLG","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:f5246f4c5ea78dac38aaeb83c598266319e453d7cbac387ee0ec076f5d131708","target":"graph","created_at":"2026-05-17T23:51:28Z","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 review the notion of relative Dolbeault cohomology and prove that it is canonically isomorphic with the local (relative) cohomology of A. Grothendieck and M. Sato with coefficients in the sheaf of holomorphic forms. We deal with this cohomology from two viewpoints. One is the Cech theoretical approach, which is convenient to define such operations as the cup product and integration and leads to the study of local duality. Along the way we also establish some notable canonical isomorphisms among various cohomologies. The other is to regard it as the cohomology of a certain complex, which is ","authors_text":"Tatsuo Suwa","cross_cats":["math.AG","math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-12T03:25:42Z","title":"Relative Dolbeault cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04710","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":"sha256:6514f78b79769f3805acd2a2bd818fb45f4885a536fd444d9c1d5419ca3f9d97","target":"record","created_at":"2026-05-17T23:51:28Z","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":"7b8427473222168394ac35f2a9b4a6035660090539ca146d423d769c69b10fa4","cross_cats_sorted":["math.AG","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-03-12T03:25:42Z","title_canon_sha256":"76e43af420420911894a9f57e1a6221246105d12de48c1852d5d8fb66e80b57c"},"schema_version":"1.0","source":{"id":"1903.04710","kind":"arxiv","version":1}},"canonical_sha256":"3026d0b166e6c50917d17cb61609807ac0f76fba5f85cad2270deb743687f549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3026d0b166e6c50917d17cb61609807ac0f76fba5f85cad2270deb743687f549","first_computed_at":"2026-05-17T23:51:28.888742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:28.888742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e+d5p7zMJMriPvD+FxR5iwSE3V8bGm+biiX+wiXt5KHq7jQJzS38FjHSLHVqtkTdmNlgJE8quTBsvKZEneh9DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:28.889338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6514f78b79769f3805acd2a2bd818fb45f4885a536fd444d9c1d5419ca3f9d97","sha256:f5246f4c5ea78dac38aaeb83c598266319e453d7cbac387ee0ec076f5d131708"],"state_sha256":"67054b8e0b537bd278e79db4d10c4dc07ef780c11f8c016b3b8e1032137fbc46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iwl8Y0YvFAGUsublmybHieod/fYodO1YDzkfNOk7Y/MIBb1uoMYWU7LkW5YLqoqpbWIQzw82NBeQdZdd8VCXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:18:00.461138Z","bundle_sha256":"077b4ad1b26a9e57badc2b542b970c54239a5d98053201d635449337eb3e0527"}}