{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YQIMRHC4HRVX5NGXD2XIS6YMHH","short_pith_number":"pith:YQIMRHC4","schema_version":"1.0","canonical_sha256":"c410c89c5c3c6b7eb4d71eae897b0c39e61881e452470a59464022dcc6299372","source":{"kind":"arxiv","id":"1410.5374","version":2},"attestation_state":"computed","paper":{"title":"Cluster algebras of infinite rank as colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sira Gratz","submitted_at":"2014-10-20T17:59:42Z","abstract_excerpt":"We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Relying on the proof of the posivity conjecture for skew-symmetric cluster algebras (of finite rank) by Lee and Schiffler, it follows as a direct consequence that the positivity conjecture holds for cluster algebras of infinite rank. Furthermore, we give a sufficient and necessary condition for a ring homomorphism between cluster algebras to give rise to a rooted cluster morphism "},"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":"1410.5374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-20T17:59:42Z","cross_cats_sorted":[],"title_canon_sha256":"ef094104d6c8b2ff6cbae3d595cbda12340af374d6886b3ed53b40ebcbfb18b2","abstract_canon_sha256":"427f1f5179f8addcbdc05798c4b3b02306146709d17514a4ef43ff649ec9cf54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:58.722904Z","signature_b64":"EOQz+5bveDTCW9LDbDff9wa6WCqK9ys7xbuo4QB5I5Bo8FHPvx2HyFo44fnIhe+F0vUNkAIPKPG1KIIX59aZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c410c89c5c3c6b7eb4d71eae897b0c39e61881e452470a59464022dcc6299372","last_reissued_at":"2026-05-18T00:39:58.722370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:58.722370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster algebras of infinite rank as colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Sira Gratz","submitted_at":"2014-10-20T17:59:42Z","abstract_excerpt":"We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Relying on the proof of the posivity conjecture for skew-symmetric cluster algebras (of finite rank) by Lee and Schiffler, it follows as a direct consequence that the positivity conjecture holds for cluster algebras of infinite rank. Furthermore, we give a sufficient and necessary condition for a ring homomorphism between cluster algebras to give rise to a rooted cluster morphism "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5374","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":""},"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":"1410.5374","created_at":"2026-05-18T00:39:58.722447+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.5374v2","created_at":"2026-05-18T00:39:58.722447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5374","created_at":"2026-05-18T00:39:58.722447+00:00"},{"alias_kind":"pith_short_12","alias_value":"YQIMRHC4HRVX","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YQIMRHC4HRVX5NGX","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YQIMRHC4","created_at":"2026-05-18T12:28:57.508820+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/YQIMRHC4HRVX5NGXD2XIS6YMHH","json":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH.json","graph_json":"https://pith.science/api/pith-number/YQIMRHC4HRVX5NGXD2XIS6YMHH/graph.json","events_json":"https://pith.science/api/pith-number/YQIMRHC4HRVX5NGXD2XIS6YMHH/events.json","paper":"https://pith.science/paper/YQIMRHC4"},"agent_actions":{"view_html":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH","download_json":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH.json","view_paper":"https://pith.science/paper/YQIMRHC4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.5374&json=true","fetch_graph":"https://pith.science/api/pith-number/YQIMRHC4HRVX5NGXD2XIS6YMHH/graph.json","fetch_events":"https://pith.science/api/pith-number/YQIMRHC4HRVX5NGXD2XIS6YMHH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH/action/storage_attestation","attest_author":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH/action/author_attestation","sign_citation":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH/action/citation_signature","submit_replication":"https://pith.science/pith/YQIMRHC4HRVX5NGXD2XIS6YMHH/action/replication_record"}},"created_at":"2026-05-18T00:39:58.722447+00:00","updated_at":"2026-05-18T00:39:58.722447+00:00"}