{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G5PLZHQQOUUSMXK4MHNIY344IE","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":"f39535ad43f39c23b5aa9be25f5b69989eba1b685ef78373c194117d379c58bc","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2014-09-29T16:25:42Z","title_canon_sha256":"3b281e1c86c5351e3dfcb57e7fa585aeb08f9c2a6bf0782fca636e34fdfe479d"},"schema_version":"1.0","source":{"id":"1409.8177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8177","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8177v2","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8177","created_at":"2026-05-18T01:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"G5PLZHQQOUUS","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G5PLZHQQOUUSMXK4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G5PLZHQQ","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:63de9ab720cb941c2f512fed5408ea91397167b00b25fcd8cfbd4cd34b2d33a7","target":"graph","created_at":"2026-05-18T01:37:49Z","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 develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.","authors_text":"Kyungyong Lee, Li Li, Matthew R. Mills","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2014-09-29T16:25:42Z","title":"A Combinatorial Formula for Certain Elements of Upper Cluster Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8177","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":"sha256:9b1ea4b4adda5f2d0e4cfa4f7021640065cf4ec61fb1b38f4371c6b11af08f0b","target":"record","created_at":"2026-05-18T01:37:49Z","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":"f39535ad43f39c23b5aa9be25f5b69989eba1b685ef78373c194117d379c58bc","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.RA","submitted_at":"2014-09-29T16:25:42Z","title_canon_sha256":"3b281e1c86c5351e3dfcb57e7fa585aeb08f9c2a6bf0782fca636e34fdfe479d"},"schema_version":"1.0","source":{"id":"1409.8177","kind":"arxiv","version":2}},"canonical_sha256":"375ebc9e107529265d5c61da8c6f9c4118a615bb55008913a55e370cde06e54f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"375ebc9e107529265d5c61da8c6f9c4118a615bb55008913a55e370cde06e54f","first_computed_at":"2026-05-18T01:37:49.340000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:49.340000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ep9pmy2GzkdnmcIsRqx+H8nc9zGx7+cGnFwzeU24+DmhNEIausuE5LAhkHXQi3cKqXiIolAn7vtrJopY8GkuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:49.340554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b1ea4b4adda5f2d0e4cfa4f7021640065cf4ec61fb1b38f4371c6b11af08f0b","sha256:63de9ab720cb941c2f512fed5408ea91397167b00b25fcd8cfbd4cd34b2d33a7"],"state_sha256":"5db8cb00b4fa356637d6de9b1441f7036d3e653005f9413ee1439192cb3fcb9e"}