{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AMRBT7XTXKN3IEQTVU24ZXUIBJ","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":"2b747154cf7341a5ce19134213119cae43eef899323a3db4550766b3abe7df68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-10T08:31:34Z","title_canon_sha256":"28b90b9f189441340a90dfd5e379e3305c57942a943c3ca577b0cc50b35e92ba"},"schema_version":"1.0","source":{"id":"1711.03724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03724","created_at":"2026-05-17T23:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03724v2","created_at":"2026-05-17T23:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03724","created_at":"2026-05-17T23:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"AMRBT7XTXKN3","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AMRBT7XTXKN3IEQT","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AMRBT7XT","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:af0a72501d0699ee57a4465b2f7f6b6a73471324c79699781d6e11bd186dc095","target":"graph","created_at":"2026-05-17T23:58:25Z","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"},"paper":{"abstract_excerpt":"We study (tame) frieze patterns over subsets of the complex numbers, with particular emphasis on the corresponding quiddity cycles. We provide new general transformations for quiddity cycles of frieze patterns. As one application, we present a combinatorial model for obtaining the quiddity cycles of all tame frieze patterns over the integers (with zero entries allowed), generalising the classic Conway-Coxeter theory. This model is thus also a model for the set of specializations of cluster algebras of Dynkin type $A$ in which all cluster variables are integers.\n  Moreover, we address the quest","authors_text":"Michael Cuntz, Thorsten Holm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-10T08:31:34Z","title":"Frieze patterns over integers and other subsets of the complex numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03724","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":"sha256:1a4ad4d897ba8c4c6f1220a7badb90ae7c2bf280835270b18a779ae14da5a384","target":"record","created_at":"2026-05-17T23:58:25Z","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":"2b747154cf7341a5ce19134213119cae43eef899323a3db4550766b3abe7df68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-10T08:31:34Z","title_canon_sha256":"28b90b9f189441340a90dfd5e379e3305c57942a943c3ca577b0cc50b35e92ba"},"schema_version":"1.0","source":{"id":"1711.03724","kind":"arxiv","version":2}},"canonical_sha256":"032219fef3ba9bb41213ad35ccde880a42337e0ed1c6fb4939a74a0f49153be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"032219fef3ba9bb41213ad35ccde880a42337e0ed1c6fb4939a74a0f49153be6","first_computed_at":"2026-05-17T23:58:25.174192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:25.174192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dbasKNfkW8oGLAN85eFbEx9fnhBKytp4rRPRDBR/e8VSCXEVc0mNQ8LrDQBiRhBn85r/mYbrDj9xoOy6fQ8cBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:25.174787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4ad4d897ba8c4c6f1220a7badb90ae7c2bf280835270b18a779ae14da5a384","sha256:af0a72501d0699ee57a4465b2f7f6b6a73471324c79699781d6e11bd186dc095"],"state_sha256":"9dd628d4ef053d7661f7ecd2cb62beca6660f8cdfc9b813d1d9011fa6114ccf5"}