{"paper":{"title":"Bockstein braiding statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math-ph","math.MP","math.QA"],"primary_cat":"quant-ph","authors_text":"Po-Shen Hsin, Yu-An Chen","submitted_at":"2026-07-02T15:00:53Z","abstract_excerpt":"Braiding statistics, from the Aharonov-Bohm phase to anyons in fractional quantum Hall systems, play a central role in quantum physics. For $p$- and $q$-dimensional excitations in $d$ spatial dimensions, ordinary braiding requires $p+q=d-2$. In a field-theoretic description of $\\mathbb Z_N$ excitations, ordinary braiding is described by the linking response $(2\\pi i/N)\\int A_{d-p}\\cup B_{d-q}$, where $A_{d-p}$ and $B_{d-q}$ are background fields coupled to the two excitation types. In this work, we identify new mutual statistics in the adjacent case $p+q=d-1$. For two invertible excitations ob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02280","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/2607.02280/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"}