{"paper":{"title":"Topological model for q-deformed rational number and categorification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Li Fan, Yu Qiu","submitted_at":"2023-05-31T18:00:03Z","abstract_excerpt":"Let $\\mathbf{D}_{3}$ be a bigraded 3-decorated disk with an arc system $\\mathbf{A}$. We associate a bigraded simple closed arc $\\widehat{\\eta}_{\\frac{r}{s}}$ on $\\mathbf{D}_{3}$ to any rational number $\\frac{r}{s}\\in\\overline{\\mathbb{Q}}=\\mathbb{Q}\\cup\\{\\infty\\}$. We show that the right (resp. left) $q$-deformed rational numbers associated to $\\frac{r}{s}$, in the sense of Morier-Genoud-Ovsienko (resp. Bapat-Becker-Licata) can be naturally calculated by the $\\mathfrak{q}$-intersection between $\\widehat{\\eta}_{\\frac{r}{s}}$ and $\\mathbf{A}$ (resp. dual arc system $\\mathbf{A}^*$). The Jones poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00063","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/2306.00063/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"}