{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VCYLVQOPLU4FZRXEWOBFUNQYEB","short_pith_number":"pith:VCYLVQOP","canonical_record":{"source":{"id":"1109.6226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-28T14:33:27Z","cross_cats_sorted":["math.AC","math.CT","math.KT","math.RA"],"title_canon_sha256":"9f33b6c382aea9dda2b47c6c6f389217c6fdb8ccc5936b42d992b42640905399","abstract_canon_sha256":"36642f872268422322d42218d858294ee7ab8414a64a119a99aab929ec4e85f6"},"schema_version":"1.0"},"canonical_sha256":"a8b0bac1cf5d385cc6e4b3825a3618205ec1589d588cb593c5d799c1a66c9ccf","source":{"kind":"arxiv","id":"1109.6226","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6226","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6226v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6226","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCYLVQOPLU4F","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VCYLVQOPLU4FZRXE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VCYLVQOP","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VCYLVQOPLU4FZRXEWOBFUNQYEB","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-28T14:33:27Z","cross_cats_sorted":["math.AC","math.CT","math.KT","math.RA"],"title_canon_sha256":"9f33b6c382aea9dda2b47c6c6f389217c6fdb8ccc5936b42d992b42640905399","abstract_canon_sha256":"36642f872268422322d42218d858294ee7ab8414a64a119a99aab929ec4e85f6"},"schema_version":"1.0"},"canonical_sha256":"a8b0bac1cf5d385cc6e4b3825a3618205ec1589d588cb593c5d799c1a66c9ccf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:09.522242Z","signature_b64":"JBFtlPcpn2aOaXuB3Hzr+npQE+ZHLw1fG2HnFhoVGfU/p0KOJNHlkpy8mav5uePAWPfbn0yLCxdn0fvBcbolDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8b0bac1cf5d385cc6e4b3825a3618205ec1589d588cb593c5d799c1a66c9ccf","last_reissued_at":"2026-05-18T04:12:09.521745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:09.521745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6226","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"keEyWIgr/Dt81DXT0fVZl+RSTTSgfDmPgzvjDo2mIEHkLFIcuFEQ/DV1nX+fXFFYjLCS/yy5I/Uk4rV03u9EDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:49:06.571903Z"},"content_sha256":"04e56e16acf17af2a809dbc088ee1d991a6d991442c19a2058d6716e30247492","schema_version":"1.0","event_id":"sha256:04e56e16acf17af2a809dbc088ee1d991a6d991442c19a2058d6716e30247492"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VCYLVQOPLU4FZRXEWOBFUNQYEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived categories and syzygies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT","math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Jiaqun Wei","submitted_at":"2011-09-28T14:33:27Z","abstract_excerpt":"We introduce syzygies for derived categories and study their properties. Using these, we prove the derived invariance of the following classes of artin algebras: (1) syzygy-finite algebras, (2) Igusa-Todorov algebras, (3) AC algebras, (4) algebras satisfying the finitistic Auslander conjecture, and (5) algebras satisfying the generalized Auslander-Reiten conjecture. In particular, Gorenstein CM-finite algebras are derived invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6226","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T04:12:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvMzZJo5aFSTkXNGpFbCtZ9lzPglA0A4sVHDyOY9Yhas2u6oqZwwxoAPZU7+FsfiOh2EO0Equ8Txi8V5SGlvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:49:06.572244Z"},"content_sha256":"b1978cec5a1dfa5b0346a081fdf11f60be6129a59ec25c3b18f0b7ab09170468","schema_version":"1.0","event_id":"sha256:b1978cec5a1dfa5b0346a081fdf11f60be6129a59ec25c3b18f0b7ab09170468"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/bundle.json","state_url":"https://pith.science/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/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":"2026-06-24T21:49:06Z","links":{"resolver":"https://pith.science/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB","bundle":"https://pith.science/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/bundle.json","state":"https://pith.science/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCYLVQOPLU4FZRXEWOBFUNQYEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VCYLVQOPLU4FZRXEWOBFUNQYEB","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":"36642f872268422322d42218d858294ee7ab8414a64a119a99aab929ec4e85f6","cross_cats_sorted":["math.AC","math.CT","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-28T14:33:27Z","title_canon_sha256":"9f33b6c382aea9dda2b47c6c6f389217c6fdb8ccc5936b42d992b42640905399"},"schema_version":"1.0","source":{"id":"1109.6226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6226","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6226v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6226","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCYLVQOPLU4F","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VCYLVQOPLU4FZRXE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VCYLVQOP","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:b1978cec5a1dfa5b0346a081fdf11f60be6129a59ec25c3b18f0b7ab09170468","target":"graph","created_at":"2026-05-18T04:12:09Z","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 introduce syzygies for derived categories and study their properties. Using these, we prove the derived invariance of the following classes of artin algebras: (1) syzygy-finite algebras, (2) Igusa-Todorov algebras, (3) AC algebras, (4) algebras satisfying the finitistic Auslander conjecture, and (5) algebras satisfying the generalized Auslander-Reiten conjecture. In particular, Gorenstein CM-finite algebras are derived invariants.","authors_text":"Jiaqun Wei","cross_cats":["math.AC","math.CT","math.KT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-28T14:33:27Z","title":"Derived categories and syzygies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6226","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":"sha256:04e56e16acf17af2a809dbc088ee1d991a6d991442c19a2058d6716e30247492","target":"record","created_at":"2026-05-18T04:12:09Z","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":"36642f872268422322d42218d858294ee7ab8414a64a119a99aab929ec4e85f6","cross_cats_sorted":["math.AC","math.CT","math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-28T14:33:27Z","title_canon_sha256":"9f33b6c382aea9dda2b47c6c6f389217c6fdb8ccc5936b42d992b42640905399"},"schema_version":"1.0","source":{"id":"1109.6226","kind":"arxiv","version":1}},"canonical_sha256":"a8b0bac1cf5d385cc6e4b3825a3618205ec1589d588cb593c5d799c1a66c9ccf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b0bac1cf5d385cc6e4b3825a3618205ec1589d588cb593c5d799c1a66c9ccf","first_computed_at":"2026-05-18T04:12:09.521745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:09.521745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JBFtlPcpn2aOaXuB3Hzr+npQE+ZHLw1fG2HnFhoVGfU/p0KOJNHlkpy8mav5uePAWPfbn0yLCxdn0fvBcbolDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:09.522242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04e56e16acf17af2a809dbc088ee1d991a6d991442c19a2058d6716e30247492","sha256:b1978cec5a1dfa5b0346a081fdf11f60be6129a59ec25c3b18f0b7ab09170468"],"state_sha256":"076c661ca030ebc8cc997a5f9c006e3afbc194935c9c67032e88e7899d152430"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w5Ii1KNPxAKm0VRwqjrXzg/IsZcKEPZ+lRBid3NDAkxDaPWGcjEx1VMghUgxe7osMrr/R1RMIIAnAf1XmcBaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:49:06.574172Z","bundle_sha256":"d9e6172262a51c52c194cbdb0018167e2777e275713770116e37deb2144ea07c"}}