{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:UZSZUPLRSVEGK2VZLM2ELULN5F","short_pith_number":"pith:UZSZUPLR","schema_version":"1.0","canonical_sha256":"a6659a3d719548656ab95b3445d16de9663a6beb3fe423a9efe95eb4999779ae","source":{"kind":"arxiv","id":"2312.15586","version":2},"attestation_state":"computed","paper":{"title":"Applications of Gorenstein projective $\\tau$-rigid modules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hui Liu, Xiaojin Zhang, Yingying Zhang","submitted_at":"2023-12-25T02:04:27Z","abstract_excerpt":"We first introduce the notion of $CM$-$\\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective $\\tau$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $\\tau$-rigid modules."},"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":"2312.15586","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-12-25T02:04:27Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"c73f391175089723b2b3218f8fb4f95a138fcda710b48e20c022665f553b65cc","abstract_canon_sha256":"144c3f59f9d8d8a856c9a5060af05ce36332f765d7ed0dc5a60c6e6ddbd771ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:28:47.861417Z","signature_b64":"aQi6tjnWAhLkpPfs9r/adA3coAEWT/C4gcKp0qmEtc8pHeYmKp4ft7c3OfG1A6mmlBytahdEtKNk5KyHUT0rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6659a3d719548656ab95b3445d16de9663a6beb3fe423a9efe95eb4999779ae","last_reissued_at":"2026-07-05T07:28:47.860929Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:28:47.860929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Applications of Gorenstein projective $\\tau$-rigid modules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hui Liu, Xiaojin Zhang, Yingying Zhang","submitted_at":"2023-12-25T02:04:27Z","abstract_excerpt":"We first introduce the notion of $CM$-$\\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective $\\tau$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $\\tau$-rigid modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.15586","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.15586/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":"2312.15586","created_at":"2026-07-05T07:28:47.860995+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.15586v2","created_at":"2026-07-05T07:28:47.860995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.15586","created_at":"2026-07-05T07:28:47.860995+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZSZUPLRSVEG","created_at":"2026-07-05T07:28:47.860995+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZSZUPLRSVEGK2VZ","created_at":"2026-07-05T07:28:47.860995+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZSZUPLR","created_at":"2026-07-05T07:28:47.860995+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/UZSZUPLRSVEGK2VZLM2ELULN5F","json":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F.json","graph_json":"https://pith.science/api/pith-number/UZSZUPLRSVEGK2VZLM2ELULN5F/graph.json","events_json":"https://pith.science/api/pith-number/UZSZUPLRSVEGK2VZLM2ELULN5F/events.json","paper":"https://pith.science/paper/UZSZUPLR"},"agent_actions":{"view_html":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F","download_json":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F.json","view_paper":"https://pith.science/paper/UZSZUPLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.15586&json=true","fetch_graph":"https://pith.science/api/pith-number/UZSZUPLRSVEGK2VZLM2ELULN5F/graph.json","fetch_events":"https://pith.science/api/pith-number/UZSZUPLRSVEGK2VZLM2ELULN5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F/action/storage_attestation","attest_author":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F/action/author_attestation","sign_citation":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F/action/citation_signature","submit_replication":"https://pith.science/pith/UZSZUPLRSVEGK2VZLM2ELULN5F/action/replication_record"}},"created_at":"2026-07-05T07:28:47.860995+00:00","updated_at":"2026-07-05T07:28:47.860995+00:00"}