{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MOBCPHA4TPFLOX7342XQAHVSNG","short_pith_number":"pith:MOBCPHA4","canonical_record":{"source":{"id":"1810.06198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-15T06:47:53Z","cross_cats_sorted":["math.AG","math.CV","math.DG","math.FA"],"title_canon_sha256":"e364d8617a2716ac1637942e2752fda82d9ee965b67cbc38c3c69837c25bb32d","abstract_canon_sha256":"10c1658dccdee17f31139f694f3cf64eac91a57e5696d5383bc4a395cecc18bb"},"schema_version":"1.0"},"canonical_sha256":"6382279c1c9bcab75ffbe6af001eb269acc365c116e63b3bd7d153bf715b057d","source":{"kind":"arxiv","id":"1810.06198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06198","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06198v1","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06198","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"MOBCPHA4TPFL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MOBCPHA4TPFLOX73","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MOBCPHA4","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MOBCPHA4TPFLOX7342XQAHVSNG","target":"record","payload":{"canonical_record":{"source":{"id":"1810.06198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-15T06:47:53Z","cross_cats_sorted":["math.AG","math.CV","math.DG","math.FA"],"title_canon_sha256":"e364d8617a2716ac1637942e2752fda82d9ee965b67cbc38c3c69837c25bb32d","abstract_canon_sha256":"10c1658dccdee17f31139f694f3cf64eac91a57e5696d5383bc4a395cecc18bb"},"schema_version":"1.0"},"canonical_sha256":"6382279c1c9bcab75ffbe6af001eb269acc365c116e63b3bd7d153bf715b057d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:21.161119Z","signature_b64":"wHjlne9bPPAXXAHL+JbidUUAEvb6yrDNHepRLCjM7+TmxniSTlLcQWvAuTHAdY44irBROLuv7VsBB2OUReZjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6382279c1c9bcab75ffbe6af001eb269acc365c116e63b3bd7d153bf715b057d","last_reissued_at":"2026-05-18T00:03:21.160659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:21.160659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.06198","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":"2026-05-18T00:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XqsE6rINJz4+2mgvt5CDGJqLAYOCBjwfA3TRkR70RAxNHluS2Qfz9j4BXA9VCIJgRkdtN+ABdGzefMd8JOPlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:32:22.908825Z"},"content_sha256":"9b66307c9f06d200e9643a4cf997a7e744009653cd9a745a29d415f8c260527c","schema_version":"1.0","event_id":"sha256:9b66307c9f06d200e9643a4cf997a7e744009653cd9a745a29d415f8c260527c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MOBCPHA4TPFLOX7342XQAHVSNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representation of relative sheaf cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.DG","math.FA"],"primary_cat":"math.AT","authors_text":"Tatsuo Suwa","submitted_at":"2018-10-15T06:47:53Z","abstract_excerpt":"We study the cohomology theory of sheaf complexes for open embeddings of topological spaces and related subjects. The theory is situated in the intersection of the general Cech theory and the theory of derived categories. That is to say, on the one hand the cohomology is described as the relative cohomology of the sections of the sheaf complex, which appears naturally in the theory of Cech cohomology of sheaf complexes. On the other hand it is interpreted as the cohomology of a complex dual to the mapping cone of a certain morphism of complexes in the theory of derived categories. We prove a \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06198","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":"2026-05-18T00:03:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kXU3q9fTbkCbf9BXVgNCUSMBdXFkMN5mC45V6zMMoHTXbVGO0YfYzO1dEAtmne1zN1gbX5GhPaaGOsRIqCvGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:32:22.909566Z"},"content_sha256":"2424f7938a63bdac66b2db65ba1567f802d91ef869e6bc8789b5927aa5c1cb98","schema_version":"1.0","event_id":"sha256:2424f7938a63bdac66b2db65ba1567f802d91ef869e6bc8789b5927aa5c1cb98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MOBCPHA4TPFLOX7342XQAHVSNG/bundle.json","state_url":"https://pith.science/pith/MOBCPHA4TPFLOX7342XQAHVSNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MOBCPHA4TPFLOX7342XQAHVSNG/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":"2026-05-31T07:32:22Z","links":{"resolver":"https://pith.science/pith/MOBCPHA4TPFLOX7342XQAHVSNG","bundle":"https://pith.science/pith/MOBCPHA4TPFLOX7342XQAHVSNG/bundle.json","state":"https://pith.science/pith/MOBCPHA4TPFLOX7342XQAHVSNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MOBCPHA4TPFLOX7342XQAHVSNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MOBCPHA4TPFLOX7342XQAHVSNG","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":"10c1658dccdee17f31139f694f3cf64eac91a57e5696d5383bc4a395cecc18bb","cross_cats_sorted":["math.AG","math.CV","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-15T06:47:53Z","title_canon_sha256":"e364d8617a2716ac1637942e2752fda82d9ee965b67cbc38c3c69837c25bb32d"},"schema_version":"1.0","source":{"id":"1810.06198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06198","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06198v1","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06198","created_at":"2026-05-18T00:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"MOBCPHA4TPFL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MOBCPHA4TPFLOX73","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MOBCPHA4","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:2424f7938a63bdac66b2db65ba1567f802d91ef869e6bc8789b5927aa5c1cb98","target":"graph","created_at":"2026-05-18T00:03:21Z","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 study the cohomology theory of sheaf complexes for open embeddings of topological spaces and related subjects. The theory is situated in the intersection of the general Cech theory and the theory of derived categories. That is to say, on the one hand the cohomology is described as the relative cohomology of the sections of the sheaf complex, which appears naturally in the theory of Cech cohomology of sheaf complexes. On the other hand it is interpreted as the cohomology of a complex dual to the mapping cone of a certain morphism of complexes in the theory of derived categories. We prove a \"","authors_text":"Tatsuo Suwa","cross_cats":["math.AG","math.CV","math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-15T06:47:53Z","title":"Representation of relative sheaf cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06198","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":"sha256:9b66307c9f06d200e9643a4cf997a7e744009653cd9a745a29d415f8c260527c","target":"record","created_at":"2026-05-18T00:03:21Z","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":"10c1658dccdee17f31139f694f3cf64eac91a57e5696d5383bc4a395cecc18bb","cross_cats_sorted":["math.AG","math.CV","math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-15T06:47:53Z","title_canon_sha256":"e364d8617a2716ac1637942e2752fda82d9ee965b67cbc38c3c69837c25bb32d"},"schema_version":"1.0","source":{"id":"1810.06198","kind":"arxiv","version":1}},"canonical_sha256":"6382279c1c9bcab75ffbe6af001eb269acc365c116e63b3bd7d153bf715b057d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6382279c1c9bcab75ffbe6af001eb269acc365c116e63b3bd7d153bf715b057d","first_computed_at":"2026-05-18T00:03:21.160659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:21.160659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wHjlne9bPPAXXAHL+JbidUUAEvb6yrDNHepRLCjM7+TmxniSTlLcQWvAuTHAdY44irBROLuv7VsBB2OUReZjAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:21.161119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b66307c9f06d200e9643a4cf997a7e744009653cd9a745a29d415f8c260527c","sha256:2424f7938a63bdac66b2db65ba1567f802d91ef869e6bc8789b5927aa5c1cb98"],"state_sha256":"da1ea5d6deaf47798f60837962cbb079506ead034d7f26c3ad2792cdf0c641c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psNXQIK/ZFVItjyMNUYjIZouFyi7KlKlf7ybzq0/DCRVwpw0BAqGzhJAo2mi3DChi/f91vBPR0e1efOUCIZsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:32:22.913763Z","bundle_sha256":"2950558908d4394f66c14a10013d8c62ff37a33fd2d775afdef25ea7d444691a"}}