{"paper":{"title":"Wilson Holonomy and Spectral Monodromy in Spin-Orbit Rings: Effective Gauge Connections and Loop Observables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"N. Bolivar","submitted_at":"2026-05-31T05:37:40Z","abstract_excerpt":"A spin-orbit Hamiltonian with an effective gauge structure carries two distinct loop objects that are routinely conflated: an energy-independent Wilson holonomy, which organizes interference and internal spin transport, and an energy-dependent monodromy, which quantizes the spectrum. We show that cleanly separating these objects supplies a precise, computable bridge between the loop/holonomy representation of gauge theories and condensed-matter spin-orbit transport. The construction maps a spin-orbit Hamiltonian to an effective $U(1)$ plus internal non-Abelian connection, reduces it to a first"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01029","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/2606.01029/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"}