{"paper":{"title":"A categorification of Kauffman states for planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GN"],"primary_cat":"math.RT","authors_text":"Domenico Fiorenza, Eugenio Landi, Giovanni Cerulli Irelli, Michele Matteucci","submitted_at":"2026-05-19T14:02:30Z","abstract_excerpt":"Given a decorated planar graph $(G,\\omega)$, where $G$ is a planar graph and $\\omega\\in H^1(|\\mathcal{Q}G|,\\mathbb{Z})$ with $\\mathcal{Q}G$ the directed medial graph of $G$, we call some angular functions $\\omega$-compatible and study two distinct but related directed graphs: $\\mathcal{L}(G,\\omega)$, which is the directed graph of such functions, and $BMS(G,\\omega)$, the directed graph of BMS states which are some pairs of $\\omega$-compatible functions plus additional data. We give sufficient conditions for $\\mathcal{L}(G,\\omega)$ to be a graded distributive lattice, recovering Kauffman's Cloc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19872","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/2605.19872/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"}