{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:BCSUSJLRESQDEFIJHELX3Z7K7E","short_pith_number":"pith:BCSUSJLR","schema_version":"1.0","canonical_sha256":"08a549257124a032150939177de7eaf9224684a40062612c434ffb99fddefee1","source":{"kind":"arxiv","id":"1410.2822","version":1},"attestation_state":"computed","paper":{"title":"Krull-Schmidt categories and projective covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Henning Krause","submitted_at":"2014-10-10T15:57:19Z","abstract_excerpt":"Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover."},"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":"1410.2822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-10T15:57:19Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"5416886cd0c363deeca986ebe3bc3f6362d1f207fc69f20bbbc3d3856426caf0","abstract_canon_sha256":"621373947d25dcade112f864f1b2f6cb229b980659107886908eb56c08f754a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:37.093894Z","signature_b64":"0SxjKIx43WPtGG1+Kn9S2QkapC7Q8uxFCM11HnxiS6twUdft8CYZMRAP4lhX9uk60CWign6OEudK10X7joyUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08a549257124a032150939177de7eaf9224684a40062612c434ffb99fddefee1","last_reissued_at":"2026-05-18T02:40:37.093197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:37.093197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Krull-Schmidt categories and projective covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Henning Krause","submitted_at":"2014-10-10T15:57:19Z","abstract_excerpt":"Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2822","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.2822","created_at":"2026-05-18T02:40:37.093305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2822v1","created_at":"2026-05-18T02:40:37.093305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2822","created_at":"2026-05-18T02:40:37.093305+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCSUSJLRESQD","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCSUSJLRESQDEFIJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCSUSJLR","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.13137","citing_title":"Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E","json":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E.json","graph_json":"https://pith.science/api/pith-number/BCSUSJLRESQDEFIJHELX3Z7K7E/graph.json","events_json":"https://pith.science/api/pith-number/BCSUSJLRESQDEFIJHELX3Z7K7E/events.json","paper":"https://pith.science/paper/BCSUSJLR"},"agent_actions":{"view_html":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E","download_json":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E.json","view_paper":"https://pith.science/paper/BCSUSJLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2822&json=true","fetch_graph":"https://pith.science/api/pith-number/BCSUSJLRESQDEFIJHELX3Z7K7E/graph.json","fetch_events":"https://pith.science/api/pith-number/BCSUSJLRESQDEFIJHELX3Z7K7E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E/action/storage_attestation","attest_author":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E/action/author_attestation","sign_citation":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E/action/citation_signature","submit_replication":"https://pith.science/pith/BCSUSJLRESQDEFIJHELX3Z7K7E/action/replication_record"}},"created_at":"2026-05-18T02:40:37.093305+00:00","updated_at":"2026-05-18T02:40:37.093305+00:00"}