{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W7YW227YJ3WBEZGFWRKSAPHDO3","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":"e1b3e745e87c606e201d7c8b142d9ed0e1c9f91bc10c9f5c6df4af6dc4683260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T14:56:57Z","title_canon_sha256":"505c8f549af2febd9588d531a1853d97de4e4b0a24377cee88f974361ae5d406"},"schema_version":"1.0","source":{"id":"1503.00289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00289","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00289v1","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00289","created_at":"2026-05-18T02:25:54Z"},{"alias_kind":"pith_short_12","alias_value":"W7YW227YJ3WB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W7YW227YJ3WBEZGF","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W7YW227Y","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:712992f821ff11b39a7dfd68995013e169c00bf49f2d9c448871d71ce7d54402","target":"graph","created_at":"2026-05-18T02:25:54Z","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":"A.Goncharov and R.Kenyon has defined a class of integrable system on a cluster varieties constructed out of a Newton polygon on the plane. In the present note we show that thiest cluster varieties coincides with the configuration spaces of collections of complete flags in an infinite dimensional space invariant with respect to two commuting operators. We use this interpretation to give explicit solution for these integrable systems in terms of theta-functions.","authors_text":"V.V.Fock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T14:56:57Z","title":"Inverse spectral problem for GK integrable system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00289","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":"sha256:007fd7da15c3cc223b1b0161e3b1d29fdd10c12d368b1ab4fe913783adaf387c","target":"record","created_at":"2026-05-18T02:25:54Z","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":"e1b3e745e87c606e201d7c8b142d9ed0e1c9f91bc10c9f5c6df4af6dc4683260","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T14:56:57Z","title_canon_sha256":"505c8f549af2febd9588d531a1853d97de4e4b0a24377cee88f974361ae5d406"},"schema_version":"1.0","source":{"id":"1503.00289","kind":"arxiv","version":1}},"canonical_sha256":"b7f16d6bf84eec1264c5b455203ce376d67685cadd033eb6644b413812988ac2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f16d6bf84eec1264c5b455203ce376d67685cadd033eb6644b413812988ac2","first_computed_at":"2026-05-18T02:25:54.752666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:54.752666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"abz2hSRvkSNQ6CDxvV7/8a1KksrGgF9r6Jja+jWn+QloJAI4uOYE+53jKxhEmK5UXegYZwACEvPEp+rS7KH/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:54.753176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:007fd7da15c3cc223b1b0161e3b1d29fdd10c12d368b1ab4fe913783adaf387c","sha256:712992f821ff11b39a7dfd68995013e169c00bf49f2d9c448871d71ce7d54402"],"state_sha256":"afff8846b6ea0040f1313011d8e02ba1c393acfc0c31b87639aaa6eb8387943e"}