{"paper":{"title":"Hodge Topology of Semiclassical Transport: A Coordinate-Free Geometric Framework for the Anomalous Hall Effect and Non-Linear Berry Dipole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math-ph","math.DG","math.MP"],"primary_cat":"cond-mat.mes-hall","authors_text":"Samuel L. Braunstein, Zhi-Wei Wang","submitted_at":"2026-06-30T09:36:04Z","abstract_excerpt":"We establish a coordinate-free differential geometric framework for anomalous transport in topological bands using the Hodge-de Rham decomposition of the Brillouin zone. Standard formulations face mathematical singularities (Dirac strings) when using the quantum Berry connection in bands with non-zero Chern numbers. Applying this decomposition to the Berry curvature 2-form isolates the quantized topological monopole flux from a globally smooth geometric 1-form proxy potential, $\\mathcal{A}$. Substituting this regularized potential into semiclassical transport integrals yields distinct analytic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31409","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/2606.31409/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"}