{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:PCM7PHGGDXNQFOUVSN6WSVJBQ4","short_pith_number":"pith:PCM7PHGG","schema_version":"1.0","canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","source":{"kind":"arxiv","id":"math/0411341","version":5},"attestation_state":"computed","paper":{"title":"Cluster algebras of finite type and positive symmetrizable matrices","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andrei Zelevinsky, Christof Geiss, Michael Barot","submitted_at":"2004-11-15T20:23:37Z","abstract_excerpt":"The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a c"},"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":"math/0411341","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"60ffa75849b9159e256a9ae1a25a8afd7fed938afe06f446b1e324fd5c474ace","abstract_canon_sha256":"45c691351ba477620131abda734d0fe67b2e744c775b2c04023dd277039b084e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:09.641542Z","signature_b64":"ldWIPpqYmnmR1p+ouS0sexJtww4jxGjFY6eeyDKLoily4Y+ob80vsQaRQpV72Tm0nMq1F5xSJE051PHVXxHwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","last_reissued_at":"2026-05-17T23:52:09.640956Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:09.640956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster algebras of finite type and positive symmetrizable matrices","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andrei Zelevinsky, Christof Geiss, Michael Barot","submitted_at":"2004-11-15T20:23:37Z","abstract_excerpt":"The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411341","kind":"arxiv","version":5},"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":"math/0411341","created_at":"2026-05-17T23:52:09.641037+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411341v5","created_at":"2026-05-17T23:52:09.641037+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411341","created_at":"2026-05-17T23:52:09.641037+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCM7PHGGDXNQ","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCM7PHGGDXNQFOUV","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCM7PHGG","created_at":"2026-05-18T12:25:52.687210+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/PCM7PHGGDXNQFOUVSN6WSVJBQ4","json":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4.json","graph_json":"https://pith.science/api/pith-number/PCM7PHGGDXNQFOUVSN6WSVJBQ4/graph.json","events_json":"https://pith.science/api/pith-number/PCM7PHGGDXNQFOUVSN6WSVJBQ4/events.json","paper":"https://pith.science/paper/PCM7PHGG"},"agent_actions":{"view_html":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4","download_json":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4.json","view_paper":"https://pith.science/paper/PCM7PHGG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411341&json=true","fetch_graph":"https://pith.science/api/pith-number/PCM7PHGGDXNQFOUVSN6WSVJBQ4/graph.json","fetch_events":"https://pith.science/api/pith-number/PCM7PHGGDXNQFOUVSN6WSVJBQ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/action/storage_attestation","attest_author":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/action/author_attestation","sign_citation":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/action/citation_signature","submit_replication":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/action/replication_record"}},"created_at":"2026-05-17T23:52:09.641037+00:00","updated_at":"2026-05-17T23:52:09.641037+00:00"}