{"paper":{"title":"Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Francesco Toppan, Zhanna Kuznetsova","submitted_at":"2025-11-30T09:37:15Z","abstract_excerpt":"We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups $Z_3^2$, $Z_2^p\\times Z_3^2$ for $p=1,2,3$, and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg-Wyler's color Lie (super)algebras framework the above abelian groups are the simplest ones which induce mixed brackets interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.00809","kind":"arxiv","version":3},"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/2512.00809/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"}