{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:U5MDUUF2CTX64XFDDA3WV2BGS5","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":"cfcf1b9443ad80024a14d3f065e6d59e56988ad993696e8d0cd826c98ef6c91e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-11T16:00:57Z","title_canon_sha256":"0fc46a866a222c60baa169c1813ec370379d81922c33bb45a5affc0bea90163b"},"schema_version":"1.0","source":{"id":"2411.07083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07083","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07083v2","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07083","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_12","alias_value":"U5MDUUF2CTX6","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_16","alias_value":"U5MDUUF2CTX64XFD","created_at":"2026-07-05T11:45:13Z"},{"alias_kind":"pith_short_8","alias_value":"U5MDUUF2","created_at":"2026-07-05T11:45:13Z"}],"graph_snapshots":[{"event_id":"sha256:6f7097916b5e8fb3e05e4eb4a928d32dea555b6a7dbce0274604a460d44e48f5","target":"graph","created_at":"2026-07-05T11:45:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.07083/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we consider mutations of skew-symmetrizable matrices of rank 3. Every skew-symmetrizable matrix corresponds to a weighted quiver, and we study the conditions when this quiver is always cyclic after applying mutations. In this study, the Markov constant has an essential meaning. It has already appeared in some previous works for skew-symmetric matrices.","authors_text":"Ryota Akagi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-11T16:00:57Z","title":"Cluster-cyclic condition of skew-symmetrizable matrices of rank 3 via the Markov constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07083","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:cb97cbc6cb13b482488b155e29f9886d2af32d4ae25ee7e51bbf448904252e3e","target":"record","created_at":"2026-07-05T11:45:13Z","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":"cfcf1b9443ad80024a14d3f065e6d59e56988ad993696e8d0cd826c98ef6c91e","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-11T16:00:57Z","title_canon_sha256":"0fc46a866a222c60baa169c1813ec370379d81922c33bb45a5affc0bea90163b"},"schema_version":"1.0","source":{"id":"2411.07083","kind":"arxiv","version":2}},"canonical_sha256":"a7583a50ba14efee5ca318376ae826977fe519bf88c014dc9831761fc995c6f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7583a50ba14efee5ca318376ae826977fe519bf88c014dc9831761fc995c6f9","first_computed_at":"2026-07-05T11:45:13.745645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:13.745645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9srgC5JzvYiQgmB8bnor9jlTZcyQd/x/Sh3oAjx4SzYn9pFMTQAUvjV29YlxwSsLw7cERxOIRVRnYAUNN1ACCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:13.746100Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.07083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb97cbc6cb13b482488b155e29f9886d2af32d4ae25ee7e51bbf448904252e3e","sha256:6f7097916b5e8fb3e05e4eb4a928d32dea555b6a7dbce0274604a460d44e48f5"],"state_sha256":"b1711f3fb42040c033e4a28d83349a006883a72c5e3f181cde4c36a0a0faedfe"}