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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}))"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.00314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-01T13:39:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"9853af0df6cf4c447086717f2303ccdab9e52f54d01fa5251485bf5cdedb0a2e","abstract_canon_sha256":"2539aee83d029a425dd46e0af1fc9426c3f912c453f469b592c959a66f1db72a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:00.735617Z","signature_b64":"CQjm2AxlRP5krF2g4fPTAJb1LjbbXelUVNZM7eqvBURVSRXo7Lb1l9+9i8rVYnYX8fqpsnwYcih246+yHnEcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4d31c54ab96a7d2a118ffee625b9f3830569ab84ac6a64a2160b1e9f2ec1b51","last_reissued_at":"2026-05-18T00:29:00.735145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:00.735145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special Precovered Categories of Gorenstein Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Tiwei Zhao, Zhaoyong Huang","submitted_at":"2017-12-01T13:39:23Z","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}))"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00314","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.00314","created_at":"2026-05-18T00:29:00.735209+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00314v2","created_at":"2026-05-18T00:29:00.735209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00314","created_at":"2026-05-18T00:29:00.735209+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTJRYVFLS2T5","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTJRYVFLS2T5FIIY","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTJRYVFL","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA","json":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA.json","graph_json":"https://pith.science/api/pith-number/UTJRYVFLS2T5FIIY77XGEW47HA/graph.json","events_json":"https://pith.science/api/pith-number/UTJRYVFLS2T5FIIY77XGEW47HA/events.json","paper":"https://pith.science/paper/UTJRYVFL"},"agent_actions":{"view_html":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA","download_json":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA.json","view_paper":"https://pith.science/paper/UTJRYVFL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00314&json=true","fetch_graph":"https://pith.science/api/pith-number/UTJRYVFLS2T5FIIY77XGEW47HA/graph.json","fetch_events":"https://pith.science/api/pith-number/UTJRYVFLS2T5FIIY77XGEW47HA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA/action/storage_attestation","attest_author":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA/action/author_attestation","sign_citation":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA/action/citation_signature","submit_replication":"https://pith.science/pith/UTJRYVFLS2T5FIIY77XGEW47HA/action/replication_record"}},"created_at":"2026-05-18T00:29:00.735209+00:00","updated_at":"2026-05-18T00:29:00.735209+00:00"}