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Huerta, Octavio Mendoza","submitted_at":"2024-01-13T15:25:05Z","abstract_excerpt":"Let $(\\mathcal{A,B})$ be a GP-admissible pair and $(\\mathcal{Z,W})$ be a GI-admissible pair of classes of objects in an abelian category $\\mathcal{C}$, and consider the class $\\pi\\mathcal{GP}_{(\\omega,\\mathcal{B},1)}$ of $1$-periodic $(\\omega,\\mathcal{B})$-Gorenstein projective objects, where $\\omega := \\mathcal{A} \\cap \\mathcal{B}$ and $\\nu := \\mathcal{Z} \\cap \\mathcal{W}$. We claimed in \\cite[Lem. 8.1]{HMP2023m} that the $(\\mathcal{Z,W})$-Gorenstein injective dimension of $\\pi\\mathcal{GP}_{(\\omega,\\mathcal{B},1)}$ is bounded by the $(\\mathcal{Z,W})$-Gorenstein injective dimension of $\\omega$"},"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":"2403.10525","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-01-13T15:25:05Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"54cba0b4c8c23d5a220e2d2ec5512c9c1cb2172679aa2c41a44f9592629d90e0","abstract_canon_sha256":"71f39bbeabb791a85f6fe346ffea83d5da4013d21fbd7c9a6ed4d93c8334b30b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:57:02.582485Z","signature_b64":"ameXBM1/AnbYLqHuCjW0ji2j2Liz93WuiDfG5BqBQXoBoaxcUY/r+ik2ozKOtqQ6Dk8pgaAz3xT02ssbD09rAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b3d737412baebd8f8c3a091f06319774e14ecd0b7245476a8f4d838d7363c27","last_reissued_at":"2026-07-05T07:57:02.582091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:57:02.582091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Corrigendum to \"$m$-Periodic Gorenstein objects\" [J. 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We claimed in \\cite[Lem. 8.1]{HMP2023m} that the $(\\mathcal{Z,W})$-Gorenstein injective dimension of $\\pi\\mathcal{GP}_{(\\omega,\\mathcal{B},1)}$ is bounded by the $(\\mathcal{Z,W})$-Gorenstein injective dimension of $\\omega$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.10525","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.10525/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2403.10525","created_at":"2026-07-05T07:57:02.582147+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.10525v1","created_at":"2026-07-05T07:57:02.582147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.10525","created_at":"2026-07-05T07:57:02.582147+00:00"},{"alias_kind":"pith_short_12","alias_value":"LM6XG5ASXLV5","created_at":"2026-07-05T07:57:02.582147+00:00"},{"alias_kind":"pith_short_16","alias_value":"LM6XG5ASXLV5R6GD","created_at":"2026-07-05T07:57:02.582147+00:00"},{"alias_kind":"pith_short_8","alias_value":"LM6XG5AS","created_at":"2026-07-05T07:57:02.582147+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/LM6XG5ASXLV5R6GDUCI7AYYZO5","json":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5.json","graph_json":"https://pith.science/api/pith-number/LM6XG5ASXLV5R6GDUCI7AYYZO5/graph.json","events_json":"https://pith.science/api/pith-number/LM6XG5ASXLV5R6GDUCI7AYYZO5/events.json","paper":"https://pith.science/paper/LM6XG5AS"},"agent_actions":{"view_html":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5","download_json":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5.json","view_paper":"https://pith.science/paper/LM6XG5AS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.10525&json=true","fetch_graph":"https://pith.science/api/pith-number/LM6XG5ASXLV5R6GDUCI7AYYZO5/graph.json","fetch_events":"https://pith.science/api/pith-number/LM6XG5ASXLV5R6GDUCI7AYYZO5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5/action/storage_attestation","attest_author":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5/action/author_attestation","sign_citation":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5/action/citation_signature","submit_replication":"https://pith.science/pith/LM6XG5ASXLV5R6GDUCI7AYYZO5/action/replication_record"}},"created_at":"2026-07-05T07:57:02.582147+00:00","updated_at":"2026-07-05T07:57:02.582147+00:00"}