{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UTJRYVFLS2T5FIIY77XGEW47HA","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":"2539aee83d029a425dd46e0af1fc9426c3f912c453f469b592c959a66f1db72a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-01T13:39:23Z","title_canon_sha256":"9853af0df6cf4c447086717f2303ccdab9e52f54d01fa5251485bf5cdedb0a2e"},"schema_version":"1.0","source":{"id":"1712.00314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00314","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00314v2","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00314","created_at":"2026-05-18T00:29:00Z"},{"alias_kind":"pith_short_12","alias_value":"UTJRYVFLS2T5","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UTJRYVFLS2T5FIIY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UTJRYVFL","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:fea3784d1e0658f1f54d0f0c63a51d03bd673544b6695a275b7db1fb73cf12e2","target":"graph","created_at":"2026-05-18T00:29:00Z","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 $\\mathscr{P}(\\mathscr{A})$ the subcategory of $\\mathscr{A}$ consisting of projective objects. Let $\\mathscr{C}$ be a full, additive and self-orthogonal subcategory of $\\mathscr{A}$ with $\\mathscr{P}(\\mathscr{A})$ a generator, and let $\\mathcal{G}(\\mathscr{C})$ be the Gorenstein subcategory of $\\mathscr{A}$. Then the right 1-orthogonal category ${\\mathcal{G}(\\mathscr{C})^{\\bot_1}}$ of $\\mathcal{G}(\\mathscr{C})$ is both projectively resolving and injectively coresolving in $\\mathscr{A}$. We also get that the subcategory $\\spc(\\mathcal{G}(\\mathscr{C}))","authors_text":"Tiwei Zhao, Zhaoyong Huang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-01T13:39:23Z","title":"Special Precovered Categories of Gorenstein Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00314","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":"sha256:23dc17119237a210a5022f685fb08f94a100c688118019025b168375be8e8000","target":"record","created_at":"2026-05-18T00:29:00Z","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":"2539aee83d029a425dd46e0af1fc9426c3f912c453f469b592c959a66f1db72a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-01T13:39:23Z","title_canon_sha256":"9853af0df6cf4c447086717f2303ccdab9e52f54d01fa5251485bf5cdedb0a2e"},"schema_version":"1.0","source":{"id":"1712.00314","kind":"arxiv","version":2}},"canonical_sha256":"a4d31c54ab96a7d2a118ffee625b9f3830569ab84ac6a64a2160b1e9f2ec1b51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4d31c54ab96a7d2a118ffee625b9f3830569ab84ac6a64a2160b1e9f2ec1b51","first_computed_at":"2026-05-18T00:29:00.735145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:00.735145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CQjm2AxlRP5krF2g4fPTAJb1LjbbXelUVNZM7eqvBURVSRXo7Lb1l9+9i8rVYnYX8fqpsnwYcih246+yHnEcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:00.735617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23dc17119237a210a5022f685fb08f94a100c688118019025b168375be8e8000","sha256:fea3784d1e0658f1f54d0f0c63a51d03bd673544b6695a275b7db1fb73cf12e2"],"state_sha256":"62ab5df0bc121d2a3edb4f16c8f501276de39190562c772c608376dac0607084"}