{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:P7AVKBR74J5HKCN4E4BTRRJFOU","short_pith_number":"pith:P7AVKBR7","schema_version":"1.0","canonical_sha256":"7fc155063fe27a7509bc270338c5257526f2223725dd59e054647c94d22adebc","source":{"kind":"arxiv","id":"1006.4592","version":4},"attestation_state":"computed","paper":{"title":"$n$-angulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.KT","authors_text":"Bernhard Keller, Christof Geiss, Steffen Oppermann","submitted_at":"2010-06-23T17:19:05Z","abstract_excerpt":"We define $n$-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$n$-angulations. We obtain a large class of examples of $n$-angulated categories by considering $(n-2)$-cluster tilting subcategories of triangulated categories which are stable under the $(n-2)$nd power of the suspension functor. As an application, we show how $n$-angulated Calabi-Yau categories yield triangulated Calabi-Yau categories of higher Calabi-Yau dimension. Finally, we sketch a link to algebraic geometry an"},"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":"1006.4592","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-06-23T17:19:05Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"92fed32a0957b7cb3ad3642ca5f318784896bc119c75825fa6d00148c0b84574","abstract_canon_sha256":"3353a167442fe4728acb5babd70f1c8dd678e11d8a2216d294a4635a5a0b0e4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:50.231935Z","signature_b64":"NN5HlIPNVlXM3X0CJIlfyTjP0AgIDDZnKdBcQWKVpJufjcQje8rvbmYFaun3HP/VJsPmEbi0RbCceGXCFFB4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fc155063fe27a7509bc270338c5257526f2223725dd59e054647c94d22adebc","last_reissued_at":"2026-05-17T23:40:50.230987Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:50.230987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$n$-angulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.KT","authors_text":"Bernhard Keller, Christof Geiss, Steffen Oppermann","submitted_at":"2010-06-23T17:19:05Z","abstract_excerpt":"We define $n$-angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$n$-angulations. We obtain a large class of examples of $n$-angulated categories by considering $(n-2)$-cluster tilting subcategories of triangulated categories which are stable under the $(n-2)$nd power of the suspension functor. As an application, we show how $n$-angulated Calabi-Yau categories yield triangulated Calabi-Yau categories of higher Calabi-Yau dimension. Finally, we sketch a link to algebraic geometry an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4592","kind":"arxiv","version":4},"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":"1006.4592","created_at":"2026-05-17T23:40:50.231368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.4592v4","created_at":"2026-05-17T23:40:50.231368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4592","created_at":"2026-05-17T23:40:50.231368+00:00"},{"alias_kind":"pith_short_12","alias_value":"P7AVKBR74J5H","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"P7AVKBR74J5HKCN4","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"P7AVKBR7","created_at":"2026-05-18T12:26:12.377268+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/P7AVKBR74J5HKCN4E4BTRRJFOU","json":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU.json","graph_json":"https://pith.science/api/pith-number/P7AVKBR74J5HKCN4E4BTRRJFOU/graph.json","events_json":"https://pith.science/api/pith-number/P7AVKBR74J5HKCN4E4BTRRJFOU/events.json","paper":"https://pith.science/paper/P7AVKBR7"},"agent_actions":{"view_html":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU","download_json":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU.json","view_paper":"https://pith.science/paper/P7AVKBR7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.4592&json=true","fetch_graph":"https://pith.science/api/pith-number/P7AVKBR74J5HKCN4E4BTRRJFOU/graph.json","fetch_events":"https://pith.science/api/pith-number/P7AVKBR74J5HKCN4E4BTRRJFOU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU/action/storage_attestation","attest_author":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU/action/author_attestation","sign_citation":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU/action/citation_signature","submit_replication":"https://pith.science/pith/P7AVKBR74J5HKCN4E4BTRRJFOU/action/replication_record"}},"created_at":"2026-05-17T23:40:50.231368+00:00","updated_at":"2026-05-17T23:40:50.231368+00:00"}