{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:27GHDV6BL2YWHPIO455ZMVJOA7","short_pith_number":"pith:27GHDV6B","schema_version":"1.0","canonical_sha256":"d7cc71d7c15eb163bd0ee77b96552e07c4af33febd189b447f3f810b8154a3c5","source":{"kind":"arxiv","id":"2303.06704","version":6},"attestation_state":"computed","paper":{"title":"Birational Weyl group actions and q-Painleve equations via mutation combinatorics in cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"nlin.SI","authors_text":"Naoto Okubo, Teruhisa Tsuda, Tetsu Masuda","submitted_at":"2023-03-12T16:50:41Z","abstract_excerpt":"A cluster algebra is an algebraic structure generated by operations of a quiver (a directed graph) called the mutations and their associated simple birational mappings. By using a graph-combinatorial approach, we present a systematic way to derive a tropical, i.e. subtraction-free birational, representation of Weyl groups from cluster algebras. Our results provide an extensive class of Weyl group actions, including previously known examples with algebro-geometric background, and hence are relevant to the q-Painleve equations and their higher-order extensions. Key ingredients of the argument ar"},"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":"2303.06704","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2023-03-12T16:50:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e49e092bf2dedea6ed55540df4b94637379327f68d0fbae5da4e4fa78ddf5ab2","abstract_canon_sha256":"ca0159502440f64a28521db4017a25aa4b93ffecc790f12b5a66e6480d3f718b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:01:17.127840Z","signature_b64":"SyyjeaKgbCwJk2bkQXqZxZmwlpWDoqp0fpVNiBFa0rdDAorHLYc0LKR3m4E8xyd3uUky7aQMYgwdyGXseTg1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7cc71d7c15eb163bd0ee77b96552e07c4af33febd189b447f3f810b8154a3c5","last_reissued_at":"2026-07-05T12:01:17.127338Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:01:17.127338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birational Weyl group actions and q-Painleve equations via mutation combinatorics in cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"nlin.SI","authors_text":"Naoto Okubo, Teruhisa Tsuda, Tetsu Masuda","submitted_at":"2023-03-12T16:50:41Z","abstract_excerpt":"A cluster algebra is an algebraic structure generated by operations of a quiver (a directed graph) called the mutations and their associated simple birational mappings. By using a graph-combinatorial approach, we present a systematic way to derive a tropical, i.e. subtraction-free birational, representation of Weyl groups from cluster algebras. Our results provide an extensive class of Weyl group actions, including previously known examples with algebro-geometric background, and hence are relevant to the q-Painleve equations and their higher-order extensions. Key ingredients of the argument ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06704","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.06704/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2303.06704","created_at":"2026-07-05T12:01:17.127401+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.06704v6","created_at":"2026-07-05T12:01:17.127401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06704","created_at":"2026-07-05T12:01:17.127401+00:00"},{"alias_kind":"pith_short_12","alias_value":"27GHDV6BL2YW","created_at":"2026-07-05T12:01:17.127401+00:00"},{"alias_kind":"pith_short_16","alias_value":"27GHDV6BL2YWHPIO","created_at":"2026-07-05T12:01:17.127401+00:00"},{"alias_kind":"pith_short_8","alias_value":"27GHDV6B","created_at":"2026-07-05T12:01:17.127401+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2601.18636","citing_title":"Birational Weyl Group Action on the Symplectic Groupoid and Cluster Algebras","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04463","citing_title":"A degeneration of the $q$-Garnier system of fourth order arises from confluences in quivers","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7","json":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7.json","graph_json":"https://pith.science/api/pith-number/27GHDV6BL2YWHPIO455ZMVJOA7/graph.json","events_json":"https://pith.science/api/pith-number/27GHDV6BL2YWHPIO455ZMVJOA7/events.json","paper":"https://pith.science/paper/27GHDV6B"},"agent_actions":{"view_html":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7","download_json":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7.json","view_paper":"https://pith.science/paper/27GHDV6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.06704&json=true","fetch_graph":"https://pith.science/api/pith-number/27GHDV6BL2YWHPIO455ZMVJOA7/graph.json","fetch_events":"https://pith.science/api/pith-number/27GHDV6BL2YWHPIO455ZMVJOA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7/action/storage_attestation","attest_author":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7/action/author_attestation","sign_citation":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7/action/citation_signature","submit_replication":"https://pith.science/pith/27GHDV6BL2YWHPIO455ZMVJOA7/action/replication_record"}},"created_at":"2026-07-05T12:01:17.127401+00:00","updated_at":"2026-07-05T12:01:17.127401+00:00"}