{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2TGM6WXDHATCLKEVBPYAJDW2CK","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":"86a09ae95af7113a41c35260b3dfbaf7afaca74ad353c443a3a0fe771faf9997","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-10T16:51:03Z","title_canon_sha256":"98280fd39a8eadb7d249e4cb3e51983eea9dcdc8ebf38bc743fd8d22230a3119"},"schema_version":"1.0","source":{"id":"1309.2573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2573","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2573v2","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2573","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"2TGM6WXDHATC","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2TGM6WXDHATCLKEV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2TGM6WXD","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:303d41a84556745fe9aa1b03cd021abb6f35ec431eb04336d1e23860b75330c2","target":"graph","created_at":"2026-05-18T02:54:14Z","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 give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric type), extend Speyer's example of an upper cluster algebra which is not finitely generated, and show that the Fock-Goncharov dual basis conjecture is usually false.","authors_text":"Mark Gross, Paul Hacking, Sean Keel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-10T16:51:03Z","title":"Birational geometry of cluster algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2573","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":"sha256:0bcc108420d738fa217648b1e2ea660f09c0167bef8b358d961c72ae84c98597","target":"record","created_at":"2026-05-18T02:54:14Z","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":"86a09ae95af7113a41c35260b3dfbaf7afaca74ad353c443a3a0fe771faf9997","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-09-10T16:51:03Z","title_canon_sha256":"98280fd39a8eadb7d249e4cb3e51983eea9dcdc8ebf38bc743fd8d22230a3119"},"schema_version":"1.0","source":{"id":"1309.2573","kind":"arxiv","version":2}},"canonical_sha256":"d4cccf5ae3382625a8950bf0048eda128bca6c67c70c6b149cae06055de7eee7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4cccf5ae3382625a8950bf0048eda128bca6c67c70c6b149cae06055de7eee7","first_computed_at":"2026-05-18T02:54:14.130584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:14.130584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jsq3R/V9vMUbrZwEtZgw3femu+OCm9LcjX4EAME0Cln00o97Zc0cwQXmctV54IdCzbnMktJzlYTfa+j012eGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:14.131073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bcc108420d738fa217648b1e2ea660f09c0167bef8b358d961c72ae84c98597","sha256:303d41a84556745fe9aa1b03cd021abb6f35ec431eb04336d1e23860b75330c2"],"state_sha256":"b7493ee4bba61165e4beb6ab03ff63332675eb1192e5ee9ad4e5b94fc245db74"}