{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:62T6ZEAKDVXAOA7YZIHJMB6S4O","short_pith_number":"pith:62T6ZEAK","schema_version":"1.0","canonical_sha256":"f6a7ec900a1d6e0703f8ca0e9607d2e39d00424a8c395025ec8b044e9ff0fba6","source":{"kind":"arxiv","id":"2407.17369","version":2},"attestation_state":"computed","paper":{"title":"Metric completions of discrete cluster categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Charley Cummings, Sira Gratz","submitted_at":"2024-07-24T15:49:19Z","abstract_excerpt":"Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself."},"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":"2407.17369","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-07-24T15:49:19Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"98096d106a80054e0caf75856f2e3cf4331ba92ab1433e7cc1c7b3e0510513ef","abstract_canon_sha256":"19dfbaa0e47485b0e0a1d3be0adcac1fcce6b09ebdaf5a84c994a18aba42e604"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:32.197818Z","signature_b64":"McoU5IB3ok8D1jSjIkZT//rh5ZdGsxVRtHV0tINVNDERTDCjAKUN5dOTmP3dCiTlw67o+nAWBpxj1RJusQJeAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6a7ec900a1d6e0703f8ca0e9607d2e39d00424a8c395025ec8b044e9ff0fba6","last_reissued_at":"2026-07-05T09:10:32.197337Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:32.197337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metric completions of discrete cluster categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Charley Cummings, Sira Gratz","submitted_at":"2024-07-24T15:49:19Z","abstract_excerpt":"Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17369","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/2407.17369/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":"2407.17369","created_at":"2026-07-05T09:10:32.197398+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.17369v2","created_at":"2026-07-05T09:10:32.197398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17369","created_at":"2026-07-05T09:10:32.197398+00:00"},{"alias_kind":"pith_short_12","alias_value":"62T6ZEAKDVXA","created_at":"2026-07-05T09:10:32.197398+00:00"},{"alias_kind":"pith_short_16","alias_value":"62T6ZEAKDVXAOA7Y","created_at":"2026-07-05T09:10:32.197398+00:00"},{"alias_kind":"pith_short_8","alias_value":"62T6ZEAK","created_at":"2026-07-05T09:10:32.197398+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":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O","json":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O.json","graph_json":"https://pith.science/api/pith-number/62T6ZEAKDVXAOA7YZIHJMB6S4O/graph.json","events_json":"https://pith.science/api/pith-number/62T6ZEAKDVXAOA7YZIHJMB6S4O/events.json","paper":"https://pith.science/paper/62T6ZEAK"},"agent_actions":{"view_html":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O","download_json":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O.json","view_paper":"https://pith.science/paper/62T6ZEAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.17369&json=true","fetch_graph":"https://pith.science/api/pith-number/62T6ZEAKDVXAOA7YZIHJMB6S4O/graph.json","fetch_events":"https://pith.science/api/pith-number/62T6ZEAKDVXAOA7YZIHJMB6S4O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O/action/storage_attestation","attest_author":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O/action/author_attestation","sign_citation":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O/action/citation_signature","submit_replication":"https://pith.science/pith/62T6ZEAKDVXAOA7YZIHJMB6S4O/action/replication_record"}},"created_at":"2026-07-05T09:10:32.197398+00:00","updated_at":"2026-07-05T09:10:32.197398+00:00"}