{"paper":{"title":"Anyons and Inherently Complex F-symbols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.QA","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Jiannis K. Pachos, Matthew Buican, Peter Huston","submitted_at":"2026-07-11T07:59:23Z","abstract_excerpt":"Anyons in $2+1$ dimensions are not only characterized by exotic braiding statistics but also by intricate fusion properties. Two anyons may fuse into multiple topological charge sectors, and associativity of fusing three anyons to produce a fixed charge sector is governed by $F$-symbols. While braiding invariants, such as the modular data, are typically complex valued, a complete description of general anyon models requires understanding the arithmetic properties of its fusion associativity data as well. The $F$-symbols for many of the most common $2+1$d topological orders, including all Abeli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10181","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/2607.10181/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"}