{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:V7RDL26XLRAXX4KIG6OGIMTOMY","short_pith_number":"pith:V7RDL26X","schema_version":"1.0","canonical_sha256":"afe235ebd75c417bf148379c64326e6639674b5a396e7cb38a77b0f173d7e128","source":{"kind":"arxiv","id":"1404.4623","version":2},"attestation_state":"computed","paper":{"title":"Torsion pairs in a triangulated category generated by a spherical object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"David Pauksztello, Raquel Coelho Simoes","submitted_at":"2014-04-17T19:39:55Z","abstract_excerpt":"We extend Ng's characterisation of torsion pairs in the 2-Calabi-Yau triangulated category generated by a 2-spherical object to the characterisation of torsion pairs in the w-Calabi-Yau triangulated category, $T_w$, generated by a w-spherical object for any integer w. Inspired by the combinatorics of $T_w$ for w < 0, we also characterise the torsion pairs in a certain w-Calabi-Yau orbit category of the bounded derived category of the path algebra of Dynkin type A."},"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":"1404.4623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-17T19:39:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"30fb41c962c9b5dc6df2b283552d84bf6a3a0907680cb58b383993725d9be799","abstract_canon_sha256":"5e9266c02f2261d4e03745b163cad7f7cfbf39a95a03016f18ed98c1fba6f07a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:38.679735Z","signature_b64":"m9N3O4/qEVUwqusWxRCpZAZ+uup4/JqfrK+bkDcLs5AngLQCOwOrH48DnmVMglKdUFb80PBLA0wSmZ01Am1cBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afe235ebd75c417bf148379c64326e6639674b5a396e7cb38a77b0f173d7e128","last_reissued_at":"2026-05-18T01:27:38.679092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:38.679092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion pairs in a triangulated category generated by a spherical object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"David Pauksztello, Raquel Coelho Simoes","submitted_at":"2014-04-17T19:39:55Z","abstract_excerpt":"We extend Ng's characterisation of torsion pairs in the 2-Calabi-Yau triangulated category generated by a 2-spherical object to the characterisation of torsion pairs in the w-Calabi-Yau triangulated category, $T_w$, generated by a w-spherical object for any integer w. Inspired by the combinatorics of $T_w$ for w < 0, we also characterise the torsion pairs in a certain w-Calabi-Yau orbit category of the bounded derived category of the path algebra of Dynkin type A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4623","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":"1404.4623","created_at":"2026-05-18T01:27:38.679202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4623v2","created_at":"2026-05-18T01:27:38.679202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4623","created_at":"2026-05-18T01:27:38.679202+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7RDL26XLRAX","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7RDL26XLRAXX4KI","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7RDL26X","created_at":"2026-05-18T12:28:52.271510+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":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY","json":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY.json","graph_json":"https://pith.science/api/pith-number/V7RDL26XLRAXX4KIG6OGIMTOMY/graph.json","events_json":"https://pith.science/api/pith-number/V7RDL26XLRAXX4KIG6OGIMTOMY/events.json","paper":"https://pith.science/paper/V7RDL26X"},"agent_actions":{"view_html":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY","download_json":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY.json","view_paper":"https://pith.science/paper/V7RDL26X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4623&json=true","fetch_graph":"https://pith.science/api/pith-number/V7RDL26XLRAXX4KIG6OGIMTOMY/graph.json","fetch_events":"https://pith.science/api/pith-number/V7RDL26XLRAXX4KIG6OGIMTOMY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY/action/storage_attestation","attest_author":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY/action/author_attestation","sign_citation":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY/action/citation_signature","submit_replication":"https://pith.science/pith/V7RDL26XLRAXX4KIG6OGIMTOMY/action/replication_record"}},"created_at":"2026-05-18T01:27:38.679202+00:00","updated_at":"2026-05-18T01:27:38.679202+00:00"}