{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JIB6775KORKAZ5Q7CK7IIGPYLE","short_pith_number":"pith:JIB6775K","schema_version":"1.0","canonical_sha256":"4a03efffaa74540cf61f12be8419f8590d2e71f6c361df100518fceccfdbf59d","source":{"kind":"arxiv","id":"1906.00106","version":2},"attestation_state":"computed","paper":{"title":"Frieze varieties are invariant under Coxeter mutation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Kiyoshi Igusa, Ralf Schiffler","submitted_at":"2019-05-31T22:19:45Z","abstract_excerpt":"We define a generalized version of the frieze variety introduced by Lee, Li, Mills, Seceleanu and the second author. The generalized frieze variety is an algebraic variety determined by an acyclic quiver and a generic specialization of cluster variables in the cluster algebra for this quiver. The original frieze variety is obtained when this specialization is (1, . . . , 1). The main result is that a generalized frieze variety is determined by any generic element of any component of that variety. We also show that the \"Coxeter mutation\" cyclically permutes these components. In particular, this"},"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":"1906.00106","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-31T22:19:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"10a808dfb1cc7706b0308ffd5160ba7a3be552dcb829c77af16b39d928aa0ad9","abstract_canon_sha256":"d3d7910fae36ae8893d3fef499c8b9af25b89d6f8a6321aa219228a797655172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:17.192145Z","signature_b64":"HRcNNurukqnJcyQzYBGx2XYW3JL0QGLOuIXuZiqgEPo9Sa2iUEkHUUpzZewS2nUnIJj4ica/iUk9dtJb3HsPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a03efffaa74540cf61f12be8419f8590d2e71f6c361df100518fceccfdbf59d","last_reissued_at":"2026-05-17T23:41:17.191535Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:17.191535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Frieze varieties are invariant under Coxeter mutation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Kiyoshi Igusa, Ralf Schiffler","submitted_at":"2019-05-31T22:19:45Z","abstract_excerpt":"We define a generalized version of the frieze variety introduced by Lee, Li, Mills, Seceleanu and the second author. The generalized frieze variety is an algebraic variety determined by an acyclic quiver and a generic specialization of cluster variables in the cluster algebra for this quiver. The original frieze variety is obtained when this specialization is (1, . . . , 1). The main result is that a generalized frieze variety is determined by any generic element of any component of that variety. We also show that the \"Coxeter mutation\" cyclically permutes these components. In particular, this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00106","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":"1906.00106","created_at":"2026-05-17T23:41:17.191628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.00106v2","created_at":"2026-05-17T23:41:17.191628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00106","created_at":"2026-05-17T23:41:17.191628+00:00"},{"alias_kind":"pith_short_12","alias_value":"JIB6775KORKA","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JIB6775KORKAZ5Q7","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JIB6775K","created_at":"2026-05-18T12:33:21.387695+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/JIB6775KORKAZ5Q7CK7IIGPYLE","json":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE.json","graph_json":"https://pith.science/api/pith-number/JIB6775KORKAZ5Q7CK7IIGPYLE/graph.json","events_json":"https://pith.science/api/pith-number/JIB6775KORKAZ5Q7CK7IIGPYLE/events.json","paper":"https://pith.science/paper/JIB6775K"},"agent_actions":{"view_html":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE","download_json":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE.json","view_paper":"https://pith.science/paper/JIB6775K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.00106&json=true","fetch_graph":"https://pith.science/api/pith-number/JIB6775KORKAZ5Q7CK7IIGPYLE/graph.json","fetch_events":"https://pith.science/api/pith-number/JIB6775KORKAZ5Q7CK7IIGPYLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE/action/storage_attestation","attest_author":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE/action/author_attestation","sign_citation":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE/action/citation_signature","submit_replication":"https://pith.science/pith/JIB6775KORKAZ5Q7CK7IIGPYLE/action/replication_record"}},"created_at":"2026-05-17T23:41:17.191628+00:00","updated_at":"2026-05-17T23:41:17.191628+00:00"}