{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TE7V2UDC6R7AZZ46HWBEEF5743","short_pith_number":"pith:TE7V2UDC","canonical_record":{"source":{"id":"2103.02915","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-04T09:42:20Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"7e5c4c1f4f8bf874907867bf394c35d5e5cc5319b1486935cac72f252f37be9f","abstract_canon_sha256":"406522c45543a26e761381d86cdafb082b22fa8857533b18aa21aca096c60a5b"},"schema_version":"1.0"},"canonical_sha256":"993f5d5062f47e0ce79e3d824217bfe6e642132520c4d6b8c776a1da7fc76ebb","source":{"kind":"arxiv","id":"2103.02915","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.02915","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"2103.02915v3","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.02915","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"TE7V2UDC6R7A","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_16","alias_value":"TE7V2UDC6R7AZZ46","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_8","alias_value":"TE7V2UDC","created_at":"2026-07-05T09:41:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TE7V2UDC6R7AZZ46HWBEEF5743","target":"record","payload":{"canonical_record":{"source":{"id":"2103.02915","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-04T09:42:20Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"7e5c4c1f4f8bf874907867bf394c35d5e5cc5319b1486935cac72f252f37be9f","abstract_canon_sha256":"406522c45543a26e761381d86cdafb082b22fa8857533b18aa21aca096c60a5b"},"schema_version":"1.0"},"canonical_sha256":"993f5d5062f47e0ce79e3d824217bfe6e642132520c4d6b8c776a1da7fc76ebb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:25.183272Z","signature_b64":"NRFpzQCTFOF3KYFkT0720FsSnyhvqAFBnxZivvyh8qC1bWfhWYISOgjvAcKZQrv8qmXMqilTgzNSa7t9qZZSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"993f5d5062f47e0ce79e3d824217bfe6e642132520c4d6b8c776a1da7fc76ebb","last_reissued_at":"2026-07-05T09:41:25.182840Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:25.182840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.02915","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLqVWY7efX7OjFbDK5liB7Am6cEqgw+2UkUpG7/JoYZXRuYiWVOA6srHGyDJyomj7cl7otqHY81D7Qxha0LBBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:30:19.001282Z"},"content_sha256":"6ab6d0a3e2fb41f91ebf0d97e1155d530e11cf3faf8948330ac995f6ed44fae2","schema_version":"1.0","event_id":"sha256:6ab6d0a3e2fb41f91ebf0d97e1155d530e11cf3faf8948330ac995f6ed44fae2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TE7V2UDC6R7AZZ46HWBEEF5743","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank $r$ DT theory from rank $0$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Richard P. Thomas, Soheyla Feyzbakhsh","submitted_at":"2021-03-04T09:42:20Z","abstract_excerpt":"Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r\\ge1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2.\n  The basic technique is to reduce the ranks of sheaves by replacing them by the cokernels of their Mochizuki/Joyce-Song pairs and then use wall crossing to handle their stability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.02915","kind":"arxiv","version":3},"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/2103.02915/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":"2026-07-05T09:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0GVh9pS1UKGIPaDt7wCWJ89xGh86MniF3SRoQrDF9BauS6Jpcq51G7WuUEPF2vR6IBv76WnGaB3DXQHXbyTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:30:19.002168Z"},"content_sha256":"b3fcb38c84d765d69df6f3c3db927227adec3aeeb31ffe2157cb5a2f6fb893ee","schema_version":"1.0","event_id":"sha256:b3fcb38c84d765d69df6f3c3db927227adec3aeeb31ffe2157cb5a2f6fb893ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TE7V2UDC6R7AZZ46HWBEEF5743/bundle.json","state_url":"https://pith.science/pith/TE7V2UDC6R7AZZ46HWBEEF5743/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TE7V2UDC6R7AZZ46HWBEEF5743/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":"2026-08-16T18:30:19Z","links":{"resolver":"https://pith.science/pith/TE7V2UDC6R7AZZ46HWBEEF5743","bundle":"https://pith.science/pith/TE7V2UDC6R7AZZ46HWBEEF5743/bundle.json","state":"https://pith.science/pith/TE7V2UDC6R7AZZ46HWBEEF5743/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TE7V2UDC6R7AZZ46HWBEEF5743/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TE7V2UDC6R7AZZ46HWBEEF5743","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":"406522c45543a26e761381d86cdafb082b22fa8857533b18aa21aca096c60a5b","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-04T09:42:20Z","title_canon_sha256":"7e5c4c1f4f8bf874907867bf394c35d5e5cc5319b1486935cac72f252f37be9f"},"schema_version":"1.0","source":{"id":"2103.02915","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.02915","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"2103.02915v3","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.02915","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"TE7V2UDC6R7A","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_16","alias_value":"TE7V2UDC6R7AZZ46","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_8","alias_value":"TE7V2UDC","created_at":"2026-07-05T09:41:25Z"}],"graph_snapshots":[{"event_id":"sha256:b3fcb38c84d765d69df6f3c3db927227adec3aeeb31ffe2157cb5a2f6fb893ee","target":"graph","created_at":"2026-07-05T09:41:25Z","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/2103.02915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r\\ge1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2.\n  The basic technique is to reduce the ranks of sheaves by replacing them by the cokernels of their Mochizuki/Joyce-Song pairs and then use wall crossing to handle their stability.","authors_text":"Richard P. Thomas, Soheyla Feyzbakhsh","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-04T09:42:20Z","title":"Rank $r$ DT theory from rank $0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.02915","kind":"arxiv","version":3},"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":"sha256:6ab6d0a3e2fb41f91ebf0d97e1155d530e11cf3faf8948330ac995f6ed44fae2","target":"record","created_at":"2026-07-05T09:41:25Z","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":"406522c45543a26e761381d86cdafb082b22fa8857533b18aa21aca096c60a5b","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-03-04T09:42:20Z","title_canon_sha256":"7e5c4c1f4f8bf874907867bf394c35d5e5cc5319b1486935cac72f252f37be9f"},"schema_version":"1.0","source":{"id":"2103.02915","kind":"arxiv","version":3}},"canonical_sha256":"993f5d5062f47e0ce79e3d824217bfe6e642132520c4d6b8c776a1da7fc76ebb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"993f5d5062f47e0ce79e3d824217bfe6e642132520c4d6b8c776a1da7fc76ebb","first_computed_at":"2026-07-05T09:41:25.182840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:25.182840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NRFpzQCTFOF3KYFkT0720FsSnyhvqAFBnxZivvyh8qC1bWfhWYISOgjvAcKZQrv8qmXMqilTgzNSa7t9qZZSBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:25.183272Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.02915","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ab6d0a3e2fb41f91ebf0d97e1155d530e11cf3faf8948330ac995f6ed44fae2","sha256:b3fcb38c84d765d69df6f3c3db927227adec3aeeb31ffe2157cb5a2f6fb893ee"],"state_sha256":"4a4610734885f29339604ccd32727af217011b4053591744501b29c769466732"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/SVkRPA3g8ZotYgL5PIjnTsetngdPt2961GioEc6wLEFc3HLJMuUws3jGYwwjh+jW+9yMPVx0pXaVjf0KmbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:30:19.006627Z","bundle_sha256":"a983f8d861665b36f6a3f578ceb1d466615b98de369e0826278bb59f88e52dba"}}