{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:V3AY74SUPE4NOJZOT5SW7K4Y6F","short_pith_number":"pith:V3AY74SU","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"},"canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","source":{"kind":"arxiv","id":"2110.08606","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08606","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08606v2","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08606","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"V3AY74SUPE4N","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_16","alias_value":"V3AY74SUPE4NOJZO","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_8","alias_value":"V3AY74SU","created_at":"2026-07-05T05:28:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:V3AY74SUPE4NOJZOT5SW7K4Y6F","target":"record","payload":{"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"},"canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","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"},"source_kind":"arxiv","source_id":"2110.08606","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CV6kkYRAsi5j044zNEVa3QQej8R5D3Baq1zuHw6QUz6HhpZPgcE8NzLOyA0OsK1b0Bp5cv9BqfP+nDydnuM5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:28:43.159677Z"},"content_sha256":"44eec2bf6c59cb2997d1a70774f7b9d59fac327eec8f8a063bc218b47d073ea8","schema_version":"1.0","event_id":"sha256:44eec2bf6c59cb2997d1a70774f7b9d59fac327eec8f8a063bc218b47d073ea8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:V3AY74SUPE4NOJZOT5SW7K4Y6F","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o604eGdsBU2giXB1EVHUXr7PoiV26Pf1mxP+g5ScgC9UIKf+N0+wEwChQALrXmS+O8yfpiJCC5OXnuGnZxG2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:28:43.160184Z"},"content_sha256":"e39ba18d5f234b9d85ab3e28ad28a9ec83b984ee814a59cd0ca1ce8d7370f694","schema_version":"1.0","event_id":"sha256:e39ba18d5f234b9d85ab3e28ad28a9ec83b984ee814a59cd0ca1ce8d7370f694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/bundle.json","state_url":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T19:28:43Z","links":{"resolver":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F","bundle":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/bundle.json","state":"https://pith.science/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V3AY74SUPE4NOJZOT5SW7K4Y6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:V3AY74SUPE4NOJZOT5SW7K4Y6F","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":"9d665c0aac92b309628002c98666f51fc2a0e4333e3e4ad2c5bc63706c94cabb","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-10-16T16:30:30Z","title_canon_sha256":"0b0a032f9da8e97e06606ff04d1893e0ef93c6b56bd6f32c93e7643288604cf0"},"schema_version":"1.0","source":{"id":"2110.08606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08606","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08606v2","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08606","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"V3AY74SUPE4N","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_16","alias_value":"V3AY74SUPE4NOJZO","created_at":"2026-07-05T05:28:42Z"},{"alias_kind":"pith_short_8","alias_value":"V3AY74SU","created_at":"2026-07-05T05:28:42Z"}],"graph_snapshots":[{"event_id":"sha256:e39ba18d5f234b9d85ab3e28ad28a9ec83b984ee814a59cd0ca1ce8d7370f694","target":"graph","created_at":"2026-07-05T05:28:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.08606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Alexandra Zvonareva, Sira Gratz","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-10-16T16:30:30Z","title":"Lattices of t-structures and thick subcategories for discrete cluster categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08606","kind":"arxiv","version":2},"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":"sha256:44eec2bf6c59cb2997d1a70774f7b9d59fac327eec8f8a063bc218b47d073ea8","target":"record","created_at":"2026-07-05T05:28:42Z","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":"9d665c0aac92b309628002c98666f51fc2a0e4333e3e4ad2c5bc63706c94cabb","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-10-16T16:30:30Z","title_canon_sha256":"0b0a032f9da8e97e06606ff04d1893e0ef93c6b56bd6f32c93e7643288604cf0"},"schema_version":"1.0","source":{"id":"2110.08606","kind":"arxiv","version":2}},"canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aec18ff2547938d7272e9f656fab98f1439633917f752433852c07d98386ee44","first_computed_at":"2026-07-05T05:28:42.614889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:42.614889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hKlB+ACZGONMMe49NO3HduHrM7yWminOAaPoq4yLnWlD93+4P3LeV09I8LRZGBoY37GLscGmPdY40SD+8s62BA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:42.615471Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.08606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44eec2bf6c59cb2997d1a70774f7b9d59fac327eec8f8a063bc218b47d073ea8","sha256:e39ba18d5f234b9d85ab3e28ad28a9ec83b984ee814a59cd0ca1ce8d7370f694"],"state_sha256":"a20d4f2fda56371893c49c9bacbf38c9805abb687a5444b71331f608c8b389a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/U7b6cVXKbHaLYXYRQSZj+Sun+AdqHPZwfYGkjId6fvwPIioMgMOkXnyLwAyxdAferXgPgDd2+2nU037S4dBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:28:43.166389Z","bundle_sha256":"923fa76933f9b912dca4a87d118fae91123fdeeb74ecd1c18fbded5a4ff27e83"}}