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For two elements $u$, $v$ of the Weyl group $W$, it is known that the coordinate ring ${\\mathbb C}[G^{u,v}]$ of the double Bruhat cell $G^{u,v}=BuB\\cap B_-vB_-$ is isomorphic to a cluster algebra $\\mathcal{A}(\\textbf{i})_{{\\mathbb C}}$ [arXiv:math/0305434, arXiv:1602.00498]. In the case $u=e$, $v=c^2$ ($c$ is a Coxeter element), the algebra ${\\mathbb C}[G^{e,c^2}]$ has only finitely many cluster variables. In this article, for $G={\\rm SL}_{r+1}(\\mathbb{C})$, we obtain expl"},"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":"1703.08323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-03-24T09:31:39Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e6ebb2fa3c035c7d0b9f10744b2d7a61ac2bc733169f53dfe31f29bc414ed19b","abstract_canon_sha256":"58cb5bccb5ea7d4da1e4fa7bf15b750a0ad1f714d8e191ebd62ba4ae6957f0e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:34.374951Z","signature_b64":"bSBE2X1f8SKaGOVz5JTspf3J8aPnynpN2rDFqlok4eE28b24MjzAzteJ28VlsXNGoZmdQrN2jZehSpog9E4ODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7002e840215decf04887b2dd31bc045d7231585258b807bfd416041af78609","last_reissued_at":"2026-05-18T00:46:34.374257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:34.374257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Toshiki Nakashima, Yuki Kanakubo","submitted_at":"2017-03-24T09:31:39Z","abstract_excerpt":"Let $G$ be a simply connected simple algebraic group over $\\mathbb{C}$, $B$ and $B_-$ be its two opposite Borel subgroups. For two elements $u$, $v$ of the Weyl group $W$, it is known that the coordinate ring ${\\mathbb C}[G^{u,v}]$ of the double Bruhat cell $G^{u,v}=BuB\\cap B_-vB_-$ is isomorphic to a cluster algebra $\\mathcal{A}(\\textbf{i})_{{\\mathbb C}}$ [arXiv:math/0305434, arXiv:1602.00498]. In the case $u=e$, $v=c^2$ ($c$ is a Coxeter element), the algebra ${\\mathbb C}[G^{e,c^2}]$ has only finitely many cluster variables. In this article, for $G={\\rm SL}_{r+1}(\\mathbb{C})$, we obtain expl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08323","kind":"arxiv","version":2},"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":"1703.08323","created_at":"2026-05-18T00:46:34.374370+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08323v2","created_at":"2026-05-18T00:46:34.374370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08323","created_at":"2026-05-18T00:46:34.374370+00:00"},{"alias_kind":"pith_short_12","alias_value":"JNYAF2CAEFO6","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JNYAF2CAEFO6Z4CI","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JNYAF2CA","created_at":"2026-05-18T12:31:24.725408+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/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR","json":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR.json","graph_json":"https://pith.science/api/pith-number/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/graph.json","events_json":"https://pith.science/api/pith-number/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/events.json","paper":"https://pith.science/paper/JNYAF2CA"},"agent_actions":{"view_html":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR","download_json":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR.json","view_paper":"https://pith.science/paper/JNYAF2CA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08323&json=true","fetch_graph":"https://pith.science/api/pith-number/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/graph.json","fetch_events":"https://pith.science/api/pith-number/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/action/storage_attestation","attest_author":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/action/author_attestation","sign_citation":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/action/citation_signature","submit_replication":"https://pith.science/pith/JNYAF2CAEFO6Z4CIQ6ZN2MN4AR/action/replication_record"}},"created_at":"2026-05-18T00:46:34.374370+00:00","updated_at":"2026-05-18T00:46:34.374370+00:00"}