{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FSV6VFFXJCCDCUHOIDQR2B57WQ","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":"e324739e67dd7037b1d2318b84b52763d030d099e80431aa4009313bae446782","cross_cats_sorted":["hep-th","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-08-05T19:36:17Z","title_canon_sha256":"639d36cd1d5bbb82c0a8285923c10b8e66e64b938dd9b0eabd4757534a5c946b"},"schema_version":"1.0","source":{"id":"2108.02828","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02828","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02828v2","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02828","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"FSV6VFFXJCCD","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_16","alias_value":"FSV6VFFXJCCDCUHO","created_at":"2026-07-05T09:41:25Z"},{"alias_kind":"pith_short_8","alias_value":"FSV6VFFX","created_at":"2026-07-05T09:41:25Z"}],"graph_snapshots":[{"event_id":"sha256:a1a66914f4c4908bb6a887a192b1a2afe4ba48298a567a72d02239521b3995cf","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/2108.02828/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.\n  We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r$ on $X$ in terms of those counting sheaves of rank 1. By the MNOP conjecture they are therefore determined by the Gromov-Witten invariants of $X$.","authors_text":"Richard P. Thomas, Soheyla Feyzbakhsh","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-08-05T19:36:17Z","title":"Rank $r$ DT theory from rank $1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02828","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":"sha256:6d20f64734e077c9c52f323973203043d8de92f1d4d1b085ca81aa2de3d28a97","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":"e324739e67dd7037b1d2318b84b52763d030d099e80431aa4009313bae446782","cross_cats_sorted":["hep-th","math.SG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2021-08-05T19:36:17Z","title_canon_sha256":"639d36cd1d5bbb82c0a8285923c10b8e66e64b938dd9b0eabd4757534a5c946b"},"schema_version":"1.0","source":{"id":"2108.02828","kind":"arxiv","version":2}},"canonical_sha256":"2cabea94b748843150ee40e11d07bfb416dda79741f824badfc705cf8dd18525","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cabea94b748843150ee40e11d07bfb416dda79741f824badfc705cf8dd18525","first_computed_at":"2026-07-05T09:41:25.282748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:25.282748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zLnHs++NYOuNKw4MYZzZmtqNanzgrEWqBVUrmPytMNgeEZTCxjq2bGi2vC0NIsiEUcaYUSZisT8wwMhY8T5aCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:25.283284Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.02828","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d20f64734e077c9c52f323973203043d8de92f1d4d1b085ca81aa2de3d28a97","sha256:a1a66914f4c4908bb6a887a192b1a2afe4ba48298a567a72d02239521b3995cf"],"state_sha256":"60dc62f00ed2950913866e7bc9a2f55fc05eef417cbb6df5d6875c545315245d"}