{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SYZOX7GJFVYNUK7TDE24ZV3BS4","short_pith_number":"pith:SYZOX7GJ","schema_version":"1.0","canonical_sha256":"9632ebfcc92d70da2bf31935ccd7619727d4f3bd329d2617bc1001f4c5c75081","source":{"kind":"arxiv","id":"1108.2195","version":1},"attestation_state":"computed","paper":{"title":"Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dong Yang, Peter Jorgensen, Thorsten Holm","submitted_at":"2011-08-10T15:03:03Z","abstract_excerpt":"Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k.\n  As main results of the paper we show that for w \\leq 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas for w \\geq 1 the opposite statement holds.\n  Moreover, without any claim to originality, we observe that for w \\leq -1, the category T is"},"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":"1108.2195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-10T15:03:03Z","cross_cats_sorted":[],"title_canon_sha256":"85ae6302b39bd178102c217ff1387b4403502cec508e20f854f8040de6c0b493","abstract_canon_sha256":"f36590c97b7b7d2f47055e9cb4fda3c836631bcabd1022c7dda01b04d11a8379"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:00.653898Z","signature_b64":"RcP69XmryptQqAF/1mK/NxR9JEYiWed8QB0nsWO6E01zYa4NRwVMQkIPf01gMc8GqtE5/yJBQ0pRxi0CZZOKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9632ebfcc92d70da2bf31935ccd7619727d4f3bd329d2617bc1001f4c5c75081","last_reissued_at":"2026-05-18T02:58:00.653267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:00.653267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dong Yang, Peter Jorgensen, Thorsten Holm","submitted_at":"2011-08-10T15:03:03Z","abstract_excerpt":"Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k.\n  As main results of the paper we show that for w \\leq 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas for w \\geq 1 the opposite statement holds.\n  Moreover, without any claim to originality, we observe that for w \\leq -1, the category T is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2195","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":"1108.2195","created_at":"2026-05-18T02:58:00.653354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2195v1","created_at":"2026-05-18T02:58:00.653354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2195","created_at":"2026-05-18T02:58:00.653354+00:00"},{"alias_kind":"pith_short_12","alias_value":"SYZOX7GJFVYN","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SYZOX7GJFVYNUK7T","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SYZOX7GJ","created_at":"2026-05-18T12:26:41.206345+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/SYZOX7GJFVYNUK7TDE24ZV3BS4","json":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4.json","graph_json":"https://pith.science/api/pith-number/SYZOX7GJFVYNUK7TDE24ZV3BS4/graph.json","events_json":"https://pith.science/api/pith-number/SYZOX7GJFVYNUK7TDE24ZV3BS4/events.json","paper":"https://pith.science/paper/SYZOX7GJ"},"agent_actions":{"view_html":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4","download_json":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4.json","view_paper":"https://pith.science/paper/SYZOX7GJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2195&json=true","fetch_graph":"https://pith.science/api/pith-number/SYZOX7GJFVYNUK7TDE24ZV3BS4/graph.json","fetch_events":"https://pith.science/api/pith-number/SYZOX7GJFVYNUK7TDE24ZV3BS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4/action/storage_attestation","attest_author":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4/action/author_attestation","sign_citation":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4/action/citation_signature","submit_replication":"https://pith.science/pith/SYZOX7GJFVYNUK7TDE24ZV3BS4/action/replication_record"}},"created_at":"2026-05-18T02:58:00.653354+00:00","updated_at":"2026-05-18T02:58:00.653354+00:00"}