{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EDM5TXEPMFOTLDP6BLBXBMXZLR","short_pith_number":"pith:EDM5TXEP","schema_version":"1.0","canonical_sha256":"20d9d9dc8f615d358dfe0ac370b2f95c551d6cfad6359ee4551c745a3bba98a7","source":{"kind":"arxiv","id":"1412.5352","version":3},"attestation_state":"computed","paper":{"title":"Exotic Cluster Structures on $SL_n$ with Belavin-Drinfeld Data of Minimal Size, I. The Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Idan Eisner","submitted_at":"2014-12-17T11:53:35Z","abstract_excerpt":"Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang Baxter equation. For any non trivial Belavin-Drinfeld data of minimal size for $SL_{n}$, we give an algorithm for constructing an initial seed $\\Sigma$ in $\\mathcal{O}(SL_{n})$. The cluster structure $\\mathcal{C}=\\mathcal{C}(\\Sigma)$ is then proved to be compatible with the Poisson bra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.5352","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-12-17T11:53:35Z","cross_cats_sorted":[],"title_canon_sha256":"4f0678140289fa239fe1d41138eae06b6aec88f6e5cb1bd78cc0e4f6f4c5de4e","abstract_canon_sha256":"342399feeed1ea1881ce69e8485b169ba41009fcd59b83f8411f10ac7747e18a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:12.154497Z","signature_b64":"TBDwxgHCfNSp7uLWDTNc7ihqat7+1QmIoLy58yjH5yvq12Im+DuHZWcl9pcO04hoAhvpV7/ZNaugAcRqiWqNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20d9d9dc8f615d358dfe0ac370b2f95c551d6cfad6359ee4551c745a3bba98a7","last_reissued_at":"2026-05-18T01:03:12.153909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:12.153909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exotic Cluster Structures on $SL_n$ with Belavin-Drinfeld Data of Minimal Size, I. The Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Idan Eisner","submitted_at":"2014-12-17T11:53:35Z","abstract_excerpt":"Using the notion of compatibility between Poisson brackets and cluster structures in the coordinate rings of simple Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang Baxter equation. For any non trivial Belavin-Drinfeld data of minimal size for $SL_{n}$, we give an algorithm for constructing an initial seed $\\Sigma$ in $\\mathcal{O}(SL_{n})$. The cluster structure $\\mathcal{C}=\\mathcal{C}(\\Sigma)$ is then proved to be compatible with the Poisson bra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5352","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.5352","created_at":"2026-05-18T01:03:12.153978+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5352v3","created_at":"2026-05-18T01:03:12.153978+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5352","created_at":"2026-05-18T01:03:12.153978+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDM5TXEPMFOT","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDM5TXEPMFOTLDP6","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDM5TXEP","created_at":"2026-05-18T12:28:25.294606+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR","json":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR.json","graph_json":"https://pith.science/api/pith-number/EDM5TXEPMFOTLDP6BLBXBMXZLR/graph.json","events_json":"https://pith.science/api/pith-number/EDM5TXEPMFOTLDP6BLBXBMXZLR/events.json","paper":"https://pith.science/paper/EDM5TXEP"},"agent_actions":{"view_html":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR","download_json":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR.json","view_paper":"https://pith.science/paper/EDM5TXEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5352&json=true","fetch_graph":"https://pith.science/api/pith-number/EDM5TXEPMFOTLDP6BLBXBMXZLR/graph.json","fetch_events":"https://pith.science/api/pith-number/EDM5TXEPMFOTLDP6BLBXBMXZLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR/action/storage_attestation","attest_author":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR/action/author_attestation","sign_citation":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR/action/citation_signature","submit_replication":"https://pith.science/pith/EDM5TXEPMFOTLDP6BLBXBMXZLR/action/replication_record"}},"created_at":"2026-05-18T01:03:12.153978+00:00","updated_at":"2026-05-18T01:03:12.153978+00:00"}