{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PJEIKJ5LAN6UXJVXYDTGY62A3R","short_pith_number":"pith:PJEIKJ5L","schema_version":"1.0","canonical_sha256":"7a488527ab037d4ba6b7c0e66c7b40dc73611f3a38dfceebdd2928ba6867f9d3","source":{"kind":"arxiv","id":"1312.3659","version":2},"attestation_state":"computed","paper":{"title":"Lattice structure of torsion classes for path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gordana Todorov, Hugh Thomas, Idun Reiten, Osamu Iyama","submitted_at":"2013-12-12T21:47:41Z","abstract_excerpt":"We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices."},"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":"1312.3659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-12T21:47:41Z","cross_cats_sorted":[],"title_canon_sha256":"3c04cb3ec2da6de3040fd25ad75e1397f3029aaa7eb16d3e3348f851c6e118ff","abstract_canon_sha256":"a32b8040aff5e4c3aea79dd5ff51a9ed88f34617a6225278385bdce166d8634d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.268163Z","signature_b64":"VjEHYdYMO3uh/5+dahoU1cogsR5MmGyyJn6dPXdYWY7DLk/ETJvUEP9QlwynPr7ffn8fjeDl8WsT6DzH02fWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a488527ab037d4ba6b7c0e66c7b40dc73611f3a38dfceebdd2928ba6867f9d3","last_reissued_at":"2026-05-18T00:44:29.267551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.267551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice structure of torsion classes for path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gordana Todorov, Hugh Thomas, Idun Reiten, Osamu Iyama","submitted_at":"2013-12-12T21:47:41Z","abstract_excerpt":"We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3659","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":"1312.3659","created_at":"2026-05-18T00:44:29.267638+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.3659v2","created_at":"2026-05-18T00:44:29.267638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3659","created_at":"2026-05-18T00:44:29.267638+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJEIKJ5LAN6U","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJEIKJ5LAN6UXJVX","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJEIKJ5L","created_at":"2026-05-18T12:27:54.935989+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/PJEIKJ5LAN6UXJVXYDTGY62A3R","json":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R.json","graph_json":"https://pith.science/api/pith-number/PJEIKJ5LAN6UXJVXYDTGY62A3R/graph.json","events_json":"https://pith.science/api/pith-number/PJEIKJ5LAN6UXJVXYDTGY62A3R/events.json","paper":"https://pith.science/paper/PJEIKJ5L"},"agent_actions":{"view_html":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R","download_json":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R.json","view_paper":"https://pith.science/paper/PJEIKJ5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.3659&json=true","fetch_graph":"https://pith.science/api/pith-number/PJEIKJ5LAN6UXJVXYDTGY62A3R/graph.json","fetch_events":"https://pith.science/api/pith-number/PJEIKJ5LAN6UXJVXYDTGY62A3R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R/action/storage_attestation","attest_author":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R/action/author_attestation","sign_citation":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R/action/citation_signature","submit_replication":"https://pith.science/pith/PJEIKJ5LAN6UXJVXYDTGY62A3R/action/replication_record"}},"created_at":"2026-05-18T00:44:29.267638+00:00","updated_at":"2026-05-18T00:44:29.267638+00:00"}