{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VBDX2N6RWM2XBDMIN73LFXMSKU","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":"a04b9d654d6048b27a145d74dce7b58913b13b44c4b57d258470d1c7b35df2b9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-17T20:22:55Z","title_canon_sha256":"79bfb79fd9c3614be26dc7f5bc7f61f1176271ad7cdecdff691e388b6fa1f301"},"schema_version":"1.0","source":{"id":"1806.06441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06441","created_at":"2026-05-18T00:13:02Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06441v1","created_at":"2026-05-18T00:13:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06441","created_at":"2026-05-18T00:13:02Z"},{"alias_kind":"pith_short_12","alias_value":"VBDX2N6RWM2X","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VBDX2N6RWM2XBDMI","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VBDX2N6R","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:63dccabf60aa5492f5bb94388c04f93d7a3437f36a2484aa5aaea0e59cfa38eb","target":"graph","created_at":"2026-05-18T00:13:02Z","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":"In this survey article we explain the intricate links between Conway-Coxeter friezes and cluster combinatorics. More precisely, we provide a formula, relying solely on the shape of the frieze, describing how each individual entry in the frieze changes under cluster mutation. Moreover, we provide a combinatorial formula for the number of submodules of a string module, and with that a simple way to compute the frieze associated to a fixed cluster tilting object in a cluster category of Dynkin type $A$ in the sense of Caldero and Chapoton.","authors_text":"Eleonore Faber, Gordana Todorov, Karin Baur, Khrystyna Serhiyenko, Sira Gratz","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-17T20:22:55Z","title":"Conway-Coxeter friezes and mutation: a survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06441","kind":"arxiv","version":1},"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:d5529f4e131328d7e11a93ceb68c4433b7c2a5ab8d193d500afd056bdb7f1dea","target":"record","created_at":"2026-05-18T00:13:02Z","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":"a04b9d654d6048b27a145d74dce7b58913b13b44c4b57d258470d1c7b35df2b9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-17T20:22:55Z","title_canon_sha256":"79bfb79fd9c3614be26dc7f5bc7f61f1176271ad7cdecdff691e388b6fa1f301"},"schema_version":"1.0","source":{"id":"1806.06441","kind":"arxiv","version":1}},"canonical_sha256":"a8477d37d1b335708d886ff6b2dd9255166873734a467a3d6b0a9327ffc51776","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8477d37d1b335708d886ff6b2dd9255166873734a467a3d6b0a9327ffc51776","first_computed_at":"2026-05-18T00:13:02.392262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:02.392262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5u2HTqe8bZmiYWIgTaihP0gBcgdlrf4PlhLLLqShq4o9O4nMfQVSV+a3Hd5LVt4clDrDmX+PBgMEv1DMU/7EAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:02.392953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5529f4e131328d7e11a93ceb68c4433b7c2a5ab8d193d500afd056bdb7f1dea","sha256:63dccabf60aa5492f5bb94388c04f93d7a3437f36a2484aa5aaea0e59cfa38eb"],"state_sha256":"87ea4e3382b088e71f21ee9f751f2517e95a387759d2d4f117ddb92d135df02a"}