{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:4J7QASORNHP2XB7QKWGJ4MOVRQ","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":"83da6579dc2be763c00406ae0955697216e8b699fec37757f57b32e868acce3d","cross_cats_sorted":["math.AG","math.CO","math.SG"],"license":"","primary_cat":"math.QA","submitted_at":"2002-08-05T15:20:04Z","title_canon_sha256":"7c6415d4dcb3df11e8e6d31af525d9e455861343f4deea09f5683979aa67a1de"},"schema_version":"1.0","source":{"id":"math/0208033","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0208033","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0208033v2","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0208033","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"4J7QASORNHP2","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_16","alias_value":"4J7QASORNHP2XB7Q","created_at":"2026-07-04T14:36:21Z"},{"alias_kind":"pith_short_8","alias_value":"4J7QASOR","created_at":"2026-07-04T14:36:21Z"}],"graph_snapshots":[{"event_id":"sha256:339c1a5b4301915fa9def7f4df4e9b6755e3b250e7bb7039b4ff717d522efd8b","target":"graph","created_at":"2026-07-04T14:36:21Z","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/math/0208033/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.","authors_text":"A. Vainshtein, M. Gekhtman, M. Shapiro","cross_cats":["math.AG","math.CO","math.SG"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2002-08-05T15:20:04Z","title":"Cluster algebras and Poisson geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0208033","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:dc01a89ba5cc60184df5265a920bffe1456be7c3bf4bb707db118f0694576b34","target":"record","created_at":"2026-07-04T14:36:21Z","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":"83da6579dc2be763c00406ae0955697216e8b699fec37757f57b32e868acce3d","cross_cats_sorted":["math.AG","math.CO","math.SG"],"license":"","primary_cat":"math.QA","submitted_at":"2002-08-05T15:20:04Z","title_canon_sha256":"7c6415d4dcb3df11e8e6d31af525d9e455861343f4deea09f5683979aa67a1de"},"schema_version":"1.0","source":{"id":"math/0208033","kind":"arxiv","version":2}},"canonical_sha256":"e27f0049d169dfab87f0558c9e31d58c228c49de2ba9b0d5a66b8c166234f8f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e27f0049d169dfab87f0558c9e31d58c228c49de2ba9b0d5a66b8c166234f8f3","first_computed_at":"2026-07-04T14:36:21.790386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:21.790386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDKAIfMVyuJb7rEfLNnayblsW9WGCBq/1Qblt95ayGCYklw1q2B+iACnGA/b+gS8lkbkrAyzOC48Kh1Nd1MMDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:21.790788Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0208033","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc01a89ba5cc60184df5265a920bffe1456be7c3bf4bb707db118f0694576b34","sha256:339c1a5b4301915fa9def7f4df4e9b6755e3b250e7bb7039b4ff717d522efd8b"],"state_sha256":"18694675df0426cc15454381f62a9ae3b5294453a7f4787364539c74d6931dd3"}