{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UQQURMDHM5USV5EHBDFKXNVJDZ","short_pith_number":"pith:UQQURMDH","canonical_record":{"source":{"id":"1203.4110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-03-19T14:10:07Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"20655a1b09118755d5f5aca8293fa64a6fe57d0b188280968722688157d34e31","abstract_canon_sha256":"6cf222992f5d5bd5709cb8e2f8e5ed5efe083851541056f07883fd773bd1d78f"},"schema_version":"1.0"},"canonical_sha256":"a42148b06767692af48708caabb6a91e684124544d436d9b0fc9b87fa98145ca","source":{"kind":"arxiv","id":"1203.4110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4110","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4110v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4110","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"UQQURMDHM5US","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UQQURMDHM5USV5EH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UQQURMDH","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UQQURMDHM5USV5EHBDFKXNVJDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-03-19T14:10:07Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"20655a1b09118755d5f5aca8293fa64a6fe57d0b188280968722688157d34e31","abstract_canon_sha256":"6cf222992f5d5bd5709cb8e2f8e5ed5efe083851541056f07883fd773bd1d78f"},"schema_version":"1.0"},"canonical_sha256":"a42148b06767692af48708caabb6a91e684124544d436d9b0fc9b87fa98145ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:48.285485Z","signature_b64":"b9MR6CJJC4PJsjKFiHnTV7fUUODeG2Mh/11YQ27lzmN0QxIIsadadZEa7uHI+k+YRhuuUl0zkJtmvfD2rxpwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a42148b06767692af48708caabb6a91e684124544d436d9b0fc9b87fa98145ca","last_reissued_at":"2026-05-18T03:59:48.285097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:48.285097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4110","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgnRdD4sChRdF5LeBQ0BAlJoJr2r2sDSZAkzzxsojCrvQkdzctT9uR7YvH7sZBLMu2A85xMBCAiZC2nbHjyfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:53:48.396685Z"},"content_sha256":"cb8deb1824ca9b348d75055554b20d94f4cc6c4f8a91c00f4ad45d61454a010b","schema_version":"1.0","event_id":"sha256:cb8deb1824ca9b348d75055554b20d94f4cc6c4f8a91c00f4ad45d61454a010b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UQQURMDHM5USV5EHBDFKXNVJDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proper Resolutions and Gorenstein Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.KT","authors_text":"Zhaoyong Huang","submitted_at":"2012-03-19T14:10:07Z","abstract_excerpt":"Let $\\mathscr{A}$ be an abelian category and $\\mathscr{C}$ an additive full subcategory of $\\mathscr{A}$. We provide a method to construct a proper $\\mathscr{C}$-resolution (resp. coproper $\\mathscr{C}$-coresolution) of one term in a short exact sequence in $\\mathscr{A}$ from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category $\\mathcal{G}(\\mathscr{C})$ posed by Sather-Wagstaff, Sharif and White; and also prove that $\\mathcal{G}(\\mathscr{C})$ is closed under direct summands. In addition, we obtain some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4110","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIf8fX7tN40sUtbUJzkl1TGTyYH65NGAgEDYVLVHCJktyRZ3yr3q/GZ13fZ2Q18+Gz57H545Pk+JSCimGRA/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T21:53:48.397020Z"},"content_sha256":"487e35110567f1d836b2e217c2dbb2c5eed52b16b738974527ddf1b0b353a5ec","schema_version":"1.0","event_id":"sha256:487e35110567f1d836b2e217c2dbb2c5eed52b16b738974527ddf1b0b353a5ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/bundle.json","state_url":"https://pith.science/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/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":"2026-06-28T21:53:48Z","links":{"resolver":"https://pith.science/pith/UQQURMDHM5USV5EHBDFKXNVJDZ","bundle":"https://pith.science/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/bundle.json","state":"https://pith.science/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQQURMDHM5USV5EHBDFKXNVJDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UQQURMDHM5USV5EHBDFKXNVJDZ","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":"6cf222992f5d5bd5709cb8e2f8e5ed5efe083851541056f07883fd773bd1d78f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-03-19T14:10:07Z","title_canon_sha256":"20655a1b09118755d5f5aca8293fa64a6fe57d0b188280968722688157d34e31"},"schema_version":"1.0","source":{"id":"1203.4110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4110","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4110v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4110","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"UQQURMDHM5US","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UQQURMDHM5USV5EH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UQQURMDH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:487e35110567f1d836b2e217c2dbb2c5eed52b16b738974527ddf1b0b353a5ec","target":"graph","created_at":"2026-05-18T03:59:48Z","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 $\\mathscr{A}$ be an abelian category and $\\mathscr{C}$ an additive full subcategory of $\\mathscr{A}$. We provide a method to construct a proper $\\mathscr{C}$-resolution (resp. coproper $\\mathscr{C}$-coresolution) of one term in a short exact sequence in $\\mathscr{A}$ from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category $\\mathcal{G}(\\mathscr{C})$ posed by Sather-Wagstaff, Sharif and White; and also prove that $\\mathcal{G}(\\mathscr{C})$ is closed under direct summands. In addition, we obtain some ","authors_text":"Zhaoyong Huang","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-03-19T14:10:07Z","title":"Proper Resolutions and Gorenstein Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4110","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:cb8deb1824ca9b348d75055554b20d94f4cc6c4f8a91c00f4ad45d61454a010b","target":"record","created_at":"2026-05-18T03:59:48Z","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":"6cf222992f5d5bd5709cb8e2f8e5ed5efe083851541056f07883fd773bd1d78f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-03-19T14:10:07Z","title_canon_sha256":"20655a1b09118755d5f5aca8293fa64a6fe57d0b188280968722688157d34e31"},"schema_version":"1.0","source":{"id":"1203.4110","kind":"arxiv","version":1}},"canonical_sha256":"a42148b06767692af48708caabb6a91e684124544d436d9b0fc9b87fa98145ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a42148b06767692af48708caabb6a91e684124544d436d9b0fc9b87fa98145ca","first_computed_at":"2026-05-18T03:59:48.285097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:48.285097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9MR6CJJC4PJsjKFiHnTV7fUUODeG2Mh/11YQ27lzmN0QxIIsadadZEa7uHI+k+YRhuuUl0zkJtmvfD2rxpwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:48.285485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb8deb1824ca9b348d75055554b20d94f4cc6c4f8a91c00f4ad45d61454a010b","sha256:487e35110567f1d836b2e217c2dbb2c5eed52b16b738974527ddf1b0b353a5ec"],"state_sha256":"13fe7942bd6c8a4f2adc1aee81e78233122d4d4ff8162119ca99fe51a1159500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UM7BNErGfHVR6a/Pnira6xOFqQVdWx9bdvEcf4fsKpJzLm/5BsnYMGhuUTX1Dfq6WAuqFNPPy8MfDUSme44uDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T21:53:48.398820Z","bundle_sha256":"2fd4d66e4799aba2f7655def9e5cfbd277a08248b181e7452b6b85a0421be9de"}}