{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6J4DDRV6CW5ZJALZ42VYD2LG2F","short_pith_number":"pith:6J4DDRV6","canonical_record":{"source":{"id":"1409.7274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2014-09-25T14:41:04Z","cross_cats_sorted":[],"title_canon_sha256":"7474c555a12505010235954d30cf37988aa391fec080c57275197a429c5299f1","abstract_canon_sha256":"d9dc127632213299abafe3923972368a7e257b645a2a791ca45522c20dc70202"},"schema_version":"1.0"},"canonical_sha256":"f27831c6be15bb948179e6ab81e966d165a30deda237afd9d355bafcbb63439d","source":{"kind":"arxiv","id":"1409.7274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7274","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7274v1","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7274","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6J4DDRV6CW5Z","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6J4DDRV6CW5ZJALZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6J4DDRV6","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6J4DDRV6CW5ZJALZ42VYD2LG2F","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2014-09-25T14:41:04Z","cross_cats_sorted":[],"title_canon_sha256":"7474c555a12505010235954d30cf37988aa391fec080c57275197a429c5299f1","abstract_canon_sha256":"d9dc127632213299abafe3923972368a7e257b645a2a791ca45522c20dc70202"},"schema_version":"1.0"},"canonical_sha256":"f27831c6be15bb948179e6ab81e966d165a30deda237afd9d355bafcbb63439d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:58.760496Z","signature_b64":"YemZw3WtUKyKGxifja+PUOxs8KiGI+s7nf8Y5XEgS/5vfiJ8h/j6qZQImy9fJ417uDt1H8UWvY0oPUYlgQQGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f27831c6be15bb948179e6ab81e966d165a30deda237afd9d355bafcbb63439d","last_reissued_at":"2026-05-18T02:41:58.760073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:58.760073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7274","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":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8eJvTljIXVUyNcCymkrbmShOCu+4rtBPCN4k7INCkJH5uaoRY64UYOhhLNwD/FkTxrpjopUDw9I2yjDgshdADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:13:47.942730Z"},"content_sha256":"8ec0f8851b88411bf36c30fcaf806fce3fd760f2b79daccdd26cc933ff0a7431","schema_version":"1.0","event_id":"sha256:8ec0f8851b88411bf36c30fcaf806fce3fd760f2b79daccdd26cc933ff0a7431"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6J4DDRV6CW5ZJALZ42VYD2LG2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of Gorenstein objects in triangulated categories","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Chunli Liang, Zhanping Wang","submitted_at":"2014-09-25T14:41:04Z","abstract_excerpt":"Let $\\mathcal{C}$ be a triangulated category with a proper class $\\xi$ of triangles. Asadollahi and Salarian introduced and studied $\\xi$-Gorenstein projective and $\\xi$-Gorenstein injective objects, and developed Gorenstein homological algebra in $\\mathcal{C}$. In this paper, we further study Gorenstein homological properties for a triangulated category. First, we discuss the stability of $\\xi$-Gorenstein projective objects, and show that the subcategory $\\mathcal{GP}(\\xi)$ of all $\\xi$-Gorenstein projective objects has a strong stability. That is, an iteration of the procedure used to define"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7274","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":"2026-05-18T02:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgUajCjeCNbzNj/EdnPr7emUG2zNvWbFFWGvlxqmqWWg3n09/GIB3C7fp71T7Xft3oNVti5Cp4hW//RdOhGOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:13:47.943075Z"},"content_sha256":"b29fc6b0a9344f3984240e1589d3c6d87faab62ecd0465e1eb6a8124319d5b81","schema_version":"1.0","event_id":"sha256:b29fc6b0a9344f3984240e1589d3c6d87faab62ecd0465e1eb6a8124319d5b81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/bundle.json","state_url":"https://pith.science/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/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":"2026-05-31T02:13:47Z","links":{"resolver":"https://pith.science/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F","bundle":"https://pith.science/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/bundle.json","state":"https://pith.science/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6J4DDRV6CW5ZJALZ42VYD2LG2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6J4DDRV6CW5ZJALZ42VYD2LG2F","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":"d9dc127632213299abafe3923972368a7e257b645a2a791ca45522c20dc70202","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2014-09-25T14:41:04Z","title_canon_sha256":"7474c555a12505010235954d30cf37988aa391fec080c57275197a429c5299f1"},"schema_version":"1.0","source":{"id":"1409.7274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7274","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7274v1","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7274","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6J4DDRV6CW5Z","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6J4DDRV6CW5ZJALZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6J4DDRV6","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:b29fc6b0a9344f3984240e1589d3c6d87faab62ecd0465e1eb6a8124319d5b81","target":"graph","created_at":"2026-05-18T02:41:58Z","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":"Let $\\mathcal{C}$ be a triangulated category with a proper class $\\xi$ of triangles. Asadollahi and Salarian introduced and studied $\\xi$-Gorenstein projective and $\\xi$-Gorenstein injective objects, and developed Gorenstein homological algebra in $\\mathcal{C}$. In this paper, we further study Gorenstein homological properties for a triangulated category. First, we discuss the stability of $\\xi$-Gorenstein projective objects, and show that the subcategory $\\mathcal{GP}(\\xi)$ of all $\\xi$-Gorenstein projective objects has a strong stability. That is, an iteration of the procedure used to define","authors_text":"Chunli Liang, Zhanping Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2014-09-25T14:41:04Z","title":"Stability of Gorenstein objects in triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7274","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":"sha256:8ec0f8851b88411bf36c30fcaf806fce3fd760f2b79daccdd26cc933ff0a7431","target":"record","created_at":"2026-05-18T02:41:58Z","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":"d9dc127632213299abafe3923972368a7e257b645a2a791ca45522c20dc70202","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CT","submitted_at":"2014-09-25T14:41:04Z","title_canon_sha256":"7474c555a12505010235954d30cf37988aa391fec080c57275197a429c5299f1"},"schema_version":"1.0","source":{"id":"1409.7274","kind":"arxiv","version":1}},"canonical_sha256":"f27831c6be15bb948179e6ab81e966d165a30deda237afd9d355bafcbb63439d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f27831c6be15bb948179e6ab81e966d165a30deda237afd9d355bafcbb63439d","first_computed_at":"2026-05-18T02:41:58.760073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:58.760073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YemZw3WtUKyKGxifja+PUOxs8KiGI+s7nf8Y5XEgS/5vfiJ8h/j6qZQImy9fJ417uDt1H8UWvY0oPUYlgQQGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:58.760496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec0f8851b88411bf36c30fcaf806fce3fd760f2b79daccdd26cc933ff0a7431","sha256:b29fc6b0a9344f3984240e1589d3c6d87faab62ecd0465e1eb6a8124319d5b81"],"state_sha256":"1f5f2f680bf498731e1998d4cb16d9b7b355b290271e12ac870f476370a1d885"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3nhH6mHkEXeZToo4mHwgkdOHB+cm9aOtZScxacX/IByvs586/mGJaQyQYkv9rxCUZXdKK2kUn0QIXqYeLLhnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:13:47.945142Z","bundle_sha256":"e37b628148660bf8e869687b5330ba8555b3f02e08df1cf793bafae92c3a6a02"}}