{"paper":{"title":"A Comparison of cluster algebra structures arising from $i$-boxes and Demazure weaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.RT","authors_text":"Euiyong Park, JiSun Huh, MyungHo Kim, Woo-Seok Jung","submitted_at":"2026-06-05T17:47:02Z","abstract_excerpt":"We compare two cluster algebras related to a positive element $\\mathtt{b}$ in the braid group of finite $ADE$ type. One is the localized bosonic extension ${\\widetilde{\\mathbb{A}}}_\\mathbb{C}(\\mathtt{b})$ equipped with an initial seed arising from an admissible chain $\\mathfrak{C}$ of $i$-boxes, which is deeply connected to monoidal categorification. The other is the coordinate ring $\\mathbb{C}[X({\\underline{\\Delta}} {\\boldsymbol{i}})]$ of the braid variety $X({\\underline{\\Delta}} {\\boldsymbol{i}})$ equipped with an initial seed arising from a Demazure weave $\\mathfrak{W}$, where ${\\boldsymbol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07493","kind":"arxiv","version":1},"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/2606.07493/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"}