{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XLKA4SWCZBZS5EQUZTMD4HODLF","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":"5c1278a41187fc2a60ae94395984d80f53590446fd9e2a37aedca465d5d2cc65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-07T04:59:27Z","title_canon_sha256":"a7bab65bb2a9a2c3f959cc7edc9108a0eadc78affdb263ec34f06383c9059372"},"schema_version":"1.0","source":{"id":"1312.2058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2058","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2058v2","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2058","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"XLKA4SWCZBZS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLKA4SWCZBZS5EQU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLKA4SWC","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:534cdda072434b7b817731f95c072c61a56ffec2d27c43e25fd80062315d4e24","target":"graph","created_at":"2026-05-18T02:41:18Z","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 varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair of morphisms which are smooth with irreducible fibres.","authors_text":"Bernt Tore Jensen, Darmajid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-07T04:59:27Z","title":"Varieties of Complexes of Fixed Rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2058","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":"sha256:1529cfcca6d7d6b67211c4e6aaac3360252108acbbcbbe85a13a6a249ec85b8c","target":"record","created_at":"2026-05-18T02:41:18Z","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":"5c1278a41187fc2a60ae94395984d80f53590446fd9e2a37aedca465d5d2cc65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-07T04:59:27Z","title_canon_sha256":"a7bab65bb2a9a2c3f959cc7edc9108a0eadc78affdb263ec34f06383c9059372"},"schema_version":"1.0","source":{"id":"1312.2058","kind":"arxiv","version":2}},"canonical_sha256":"bad40e4ac2c8732e9214ccd83e1dc3596d7bc29cd2b954a984123b435444f691","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bad40e4ac2c8732e9214ccd83e1dc3596d7bc29cd2b954a984123b435444f691","first_computed_at":"2026-05-18T02:41:18.735058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.735058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eLRFBu/I8vzsjhGjsU10QmwccBTyhxXzg7rPvxMwjNG4ay3UssqwiE9jsrYJEPvLcbBppd+hbpOqh3v4+R3bBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.735497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1529cfcca6d7d6b67211c4e6aaac3360252108acbbcbbe85a13a6a249ec85b8c","sha256:534cdda072434b7b817731f95c072c61a56ffec2d27c43e25fd80062315d4e24"],"state_sha256":"b1a6219db0c31dd8cc4a46a6217130a344520754c130117c73c2a492609b32f6"}