{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XJHN3UYUACLEUYGF7QVODEML5Z","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":"a985b77f967f4fdfa9a0937e5eeb314e0516ebf81763b91192762cd8370e97b9","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-15T22:41:13Z","title_canon_sha256":"d442b6b0a292ec1bd090c9b443f06b3e7873990c2c8d58a09d143fa80e86e91f"},"schema_version":"1.0","source":{"id":"1712.06975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06975","created_at":"2026-05-18T00:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06975v1","created_at":"2026-05-18T00:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06975","created_at":"2026-05-18T00:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"XJHN3UYUACLE","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XJHN3UYUACLEUYGF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XJHN3UYU","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:2d4ca8332e06cf4125e7d8748ec3688acb292eb4aa56e48bf5dd2d37b4b43b99","target":"graph","created_at":"2026-05-18T00:27:37Z","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 paper, we prove that positivity of denominator vectors holds for any skew-symmetric cluster algebra.","authors_text":"Fang Li, Peigen Cao","cross_cats":["math.AC","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-15T22:41:13Z","title":"Positivity of denominator vectors of cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06975","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":"sha256:90e028a18c88a9b624735351e4571631eab97d98f73a68d4abc4448fbe0de285","target":"record","created_at":"2026-05-18T00:27:37Z","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":"a985b77f967f4fdfa9a0937e5eeb314e0516ebf81763b91192762cd8370e97b9","cross_cats_sorted":["math.AC","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-15T22:41:13Z","title_canon_sha256":"d442b6b0a292ec1bd090c9b443f06b3e7873990c2c8d58a09d143fa80e86e91f"},"schema_version":"1.0","source":{"id":"1712.06975","kind":"arxiv","version":1}},"canonical_sha256":"ba4eddd31400964a60c5fc2ae1918bee42a99fdac6b8243eb19e59e6ddd1618f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4eddd31400964a60c5fc2ae1918bee42a99fdac6b8243eb19e59e6ddd1618f","first_computed_at":"2026-05-18T00:27:37.566699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:37.566699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"diTr9Il5jj8l848mW5wGSqkEFQ4NtaxrqOZCtVOOn6v9o/vlM0BQYoZXARGTk3BY7KfvjKSrE54dXJCCP5iYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:37.567354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e028a18c88a9b624735351e4571631eab97d98f73a68d4abc4448fbe0de285","sha256:2d4ca8332e06cf4125e7d8748ec3688acb292eb4aa56e48bf5dd2d37b4b43b99"],"state_sha256":"592982ce570596ecc15c1c205aa37c14ad0ff1d4603c96336ff4e663e9177056"}