{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:V3AY74SUPE4NOJZOT5SW7K4Y6F","short_pith_number":"pith:V3AY74SU","schema_version":"1.0","canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","source":{"kind":"arxiv","id":"2110.08606","version":2},"attestation_state":"computed","paper":{"title":"Lattices of t-structures and thick subcategories for discrete cluster categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Alexandra Zvonareva, Sira Gratz","submitted_at":"2021-10-16T16:30:30Z","abstract_excerpt":"We classify t-structures and thick subcategories in discrete cluster categories $\\mathcal{C}(\\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\\mathcal{C}(\\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\\mathcal{C}(\\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\\mathcal{C}(\\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structur"},"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":"2110.08606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-10-16T16:30:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"0b0a032f9da8e97e06606ff04d1893e0ef93c6b56bd6f32c93e7643288604cf0","abstract_canon_sha256":"9d665c0aac92b309628002c98666f51fc2a0e4333e3e4ad2c5bc63706c94cabb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:42.615471Z","signature_b64":"hKlB+ACZGONMMe49NO3HduHrM7yWminOAaPoq4yLnWlD93+4P3LeV09I8LRZGBoY37GLscGmPdY40SD+8s62BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","last_reissued_at":"2026-07-05T05:28:42.614889Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:42.614889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattices of t-structures and thick subcategories for discrete cluster categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Alexandra Zvonareva, Sira Gratz","submitted_at":"2021-10-16T16:30:30Z","abstract_excerpt":"We classify t-structures and thick subcategories in discrete cluster categories $\\mathcal{C}(\\mathcal{Z})$ of Dynkin type $A$, and show that the set of all t-structures on $\\mathcal{C}(\\mathcal{Z})$ is a lattice under inclusion of aisles, with meet given by their intersection. We show that both the lattice of t-structures on $\\mathcal{C}(\\mathcal{Z})$ obtained in this way and the lattice of thick subcategories of $\\mathcal{C}(\\mathcal{Z})$ are intimately related to the lattice of non-crossing partitions of type $A$. In particular, the lattice of equivalence classes of non-degenerate t-structur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08606","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.08606/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2110.08606","created_at":"2026-07-05T05:28:42.614944+00:00"},{"alias_kind":"arxiv_version","alias_value":"2110.08606v2","created_at":"2026-07-05T05:28:42.614944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08606","created_at":"2026-07-05T05:28:42.614944+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3AY74SUPE4N","created_at":"2026-07-05T05:28:42.614944+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3AY74SUPE4NOJZO","created_at":"2026-07-05T05:28:42.614944+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3AY74SU","created_at":"2026-07-05T05:28:42.614944+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":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F","json":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F.json","graph_json":"https://pith.science/api/pith-number/V3AY74SUPE4NOJZOT5SW7K4Y6F/graph.json","events_json":"https://pith.science/api/pith-number/V3AY74SUPE4NOJZOT5SW7K4Y6F/events.json","paper":"https://pith.science/paper/V3AY74SU"},"agent_actions":{"view_html":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F","download_json":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F.json","view_paper":"https://pith.science/paper/V3AY74SU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2110.08606&json=true","fetch_graph":"https://pith.science/api/pith-number/V3AY74SUPE4NOJZOT5SW7K4Y6F/graph.json","fetch_events":"https://pith.science/api/pith-number/V3AY74SUPE4NOJZOT5SW7K4Y6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/action/storage_attestation","attest_author":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/action/author_attestation","sign_citation":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/action/citation_signature","submit_replication":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/action/replication_record"}},"created_at":"2026-07-05T05:28:42.614944+00:00","updated_at":"2026-07-05T05:28:42.614944+00:00"}