{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C27AEDYFD3DG5YT4GRNZBDNN5J","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":"56c331d9ac18f758308ea6816f1705d91fe931764a299640ba07a5898c54009d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-09T04:17:42Z","title_canon_sha256":"a0dcbd76b27893c90e29117982363055dedc133065404ad1498645177505647d"},"schema_version":"1.0","source":{"id":"1502.02349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02349","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02349v1","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02349","created_at":"2026-05-18T02:27:42Z"},{"alias_kind":"pith_short_12","alias_value":"C27AEDYFD3DG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C27AEDYFD3DG5YT4","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C27AEDYF","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:db432b0744eb421e4f8d8c8f388c5eb1e974c402f3aea95320304483b6387e0f","target":"graph","created_at":"2026-05-18T02:27:42Z","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 properties of the relative derived category $D_{\\mathscr{C}}^{b}$($\\mathscr{A}$) of an abelian category $\\mathscr{A}$ relative to a full and additive subcategory $\\mathscr{C}$. In particular, when $\\mathscr{A}=A{\\text -}\\mod$ for a finite-dimensional algebra $A$ over a field and $\\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\\mod$ which is admissible and closed under direct summands, the $\\mathscr{C}$-singularity category $D_{\\mathscr{C}{\\text sg}}$($\\mathscr{A}$)=$D_{\\mathscr{C}}^{b}$($\\mathscr{A}$)/$K^{b}(\\mathscr{C})$ is studied. We give a sufficient condition wh","authors_text":"Huanhuan Li, Zhaoyong Huang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-09T04:17:42Z","title":"Relative Singularity Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02349","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":"sha256:698bff4ee7dfc232b6a9f76265144d2fdaa73fa60504e1376f5068e77a48a8db","target":"record","created_at":"2026-05-18T02:27:42Z","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":"56c331d9ac18f758308ea6816f1705d91fe931764a299640ba07a5898c54009d","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-09T04:17:42Z","title_canon_sha256":"a0dcbd76b27893c90e29117982363055dedc133065404ad1498645177505647d"},"schema_version":"1.0","source":{"id":"1502.02349","kind":"arxiv","version":1}},"canonical_sha256":"16be020f051ec66ee27c345b908dadea4fabbf6b1615af08014b155484736a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16be020f051ec66ee27c345b908dadea4fabbf6b1615af08014b155484736a96","first_computed_at":"2026-05-18T02:27:42.759732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:42.759732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GihSuUS5z/lX7vYV5hViSl74XS3ToeEd986bWiAmwkNl9xkbOr9ZHTHe1D1Q8snGiLujzlZtofr86gXpO2EZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:42.760545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:698bff4ee7dfc232b6a9f76265144d2fdaa73fa60504e1376f5068e77a48a8db","sha256:db432b0744eb421e4f8d8c8f388c5eb1e974c402f3aea95320304483b6387e0f"],"state_sha256":"6069a8a15f60ad7db607be77cfff6eae932e72c6e3a70553af30caa2ca5771c0"}