{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DPNTXHTJVBXEKGPR7TWNRM6IJP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4fd9c0c882c621fe99e2750ed8e2ac5f0d776dfa92ae81ea05e011fec56de0aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T15:17:00Z","title_canon_sha256":"a07f5f30c8d456618250f50089a7f906ffe9fd7b3928f980e26b65f911a666da"},"schema_version":"1.0","source":{"id":"1710.08837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08837","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08837v1","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08837","created_at":"2026-05-18T00:32:03Z"},{"alias_kind":"pith_short_12","alias_value":"DPNTXHTJVBXE","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPNTXHTJVBXEKGPR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPNTXHTJ","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:70c714e1660fe3a4d3263a5e97a22ff7ba6cf0189cf310467c2b28fc7892eff8","target":"graph","created_at":"2026-05-18T00:32:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\Lambda$ be a finite-dimensional associative algebra. The torsion classes of $mod\\, \\Lambda$ form a lattice under containment, denoted by $tors\\, \\Lambda$. In this paper, we characterize the cover relations in $tors\\, \\Lambda$ by certain indecomposable modules. We consider three applications: First, we show that the completely join-irreducible torsion classes (torsion classes which cover precisely one element) are in bijection with bricks. Second, we characterize faces of the canonical join complex of $tors\\, \\Lambda$ in terms of representation theory. Finally, we show that, in general, t","authors_text":"Andrew T. Carroll, Emily Barnard, Shijie Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T15:17:00Z","title":"Minimal inclusions of torsion classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08837","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:776971c90dd0e7703115c6c6cc1dc63976e0bb77dd590be2fae38671983bf391","target":"record","created_at":"2026-05-18T00:32:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4fd9c0c882c621fe99e2750ed8e2ac5f0d776dfa92ae81ea05e011fec56de0aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-24T15:17:00Z","title_canon_sha256":"a07f5f30c8d456618250f50089a7f906ffe9fd7b3928f980e26b65f911a666da"},"schema_version":"1.0","source":{"id":"1710.08837","kind":"arxiv","version":1}},"canonical_sha256":"1bdb3b9e69a86e4519f1fcecd8b3c84be0ca85feec4427274c8e44809f98716b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bdb3b9e69a86e4519f1fcecd8b3c84be0ca85feec4427274c8e44809f98716b","first_computed_at":"2026-05-18T00:32:03.677588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:03.677588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rc8J/e7l5n9mhR9mk+AMVqGTn1AbNrftoCMgDlv4bm3dwaREPA0OxkFdIgnD5skoGmP6D88XuBt7d2Y+QgVWAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:03.678189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776971c90dd0e7703115c6c6cc1dc63976e0bb77dd590be2fae38671983bf391","sha256:70c714e1660fe3a4d3263a5e97a22ff7ba6cf0189cf310467c2b28fc7892eff8"],"state_sha256":"773df0f01a6bad2590b0a2e0cb6609cc805ce788ea2e9913c3cc48d458e8d3e1"}