{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LAVJVKONVCGJ33VKAM4IFX4LD4","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":"a650f72bab3409a9b9e8cdc13760b355bd0bc23f1462840ca0a33561d7c45251","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-27T19:49:32Z","title_canon_sha256":"dcd6c368696f8ecb6a6fed1622aaf8d71905ade086e930f698d8e7ff6b7d403e"},"schema_version":"1.0","source":{"id":"1601.07519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07519","created_at":"2026-05-18T01:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07519v2","created_at":"2026-05-18T01:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07519","created_at":"2026-05-18T01:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"LAVJVKONVCGJ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LAVJVKONVCGJ33VK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LAVJVKON","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:af7ee0b7205213197951d1d5fb60ffef45b20cab9e8d78089e7b9522c07df62d","target":"graph","created_at":"2026-05-18T01:21:44Z","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 remark that the combination of the works of Ben-Bassat-Brav-Bussi-Joyce and Alper-Hall-Rydh imply the conjectured local description of the moduli stacks of semi-Schur objects in the derived category of coherent sheaves on projective Calabi-Yau 3-folds. This result was assumed in the author's previous papers to apply wall-crossing formulas of DT type invariants in the derived category, e.g. DT/PT correspondence, rationality, etc. We also show that the above result is applied to prove the higher rank version of DT/PT correspondence and rationality.","authors_text":"Yukinobu Toda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-27T19:49:32Z","title":"Hall algebras in the derived category and higher rank DT invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07519","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":"sha256:2ded0eeee10ffbe1671630fb2ae11ae383586a7096c8e6c78ff5d33133ba8f58","target":"record","created_at":"2026-05-18T01:21:44Z","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":"a650f72bab3409a9b9e8cdc13760b355bd0bc23f1462840ca0a33561d7c45251","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-27T19:49:32Z","title_canon_sha256":"dcd6c368696f8ecb6a6fed1622aaf8d71905ade086e930f698d8e7ff6b7d403e"},"schema_version":"1.0","source":{"id":"1601.07519","kind":"arxiv","version":2}},"canonical_sha256":"582a9aa9cda88c9deeaa033882df8b1f1abf11548cd3a293f744e2786af506dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"582a9aa9cda88c9deeaa033882df8b1f1abf11548cd3a293f744e2786af506dd","first_computed_at":"2026-05-18T01:21:44.132426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:44.132426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4gEzfmlSnJx3HL3NTaoFkNEcGE5gHNvRP6KLJ5Gg34uEKz1D0OYpjDNgkxMiCqCFpqGjPU/Uq9WyC8DSeq1XAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:44.133124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ded0eeee10ffbe1671630fb2ae11ae383586a7096c8e6c78ff5d33133ba8f58","sha256:af7ee0b7205213197951d1d5fb60ffef45b20cab9e8d78089e7b9522c07df62d"],"state_sha256":"7a0920d2488fb4ddd4f4690335b22778c8768d439cdafa2520b2d4fe6916a1de"}