{"paper":{"title":"Higher power polyadic group rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","hep-th","math-ph","math.GR","math.IT","math.MP"],"primary_cat":"math.RA","authors_text":"Steven Duplij","submitted_at":"2025-10-15T19:10:39Z","abstract_excerpt":"This paper introduces and systematically develops the theory of polyadic group rings, a higher arity generalization of classical group rings $\\mathcal{R}[\\mathsf{G}]$. We construct the fundamental operations of these structures, defining the $\\mathbf{m}_{r}$-ary addition and $\\mathbf{n}_{r} $-ary multiplication for a polyadic group ring $\\mathrm{R}^{[\\mathbf{m} _{r},\\mathbf{n}_{r}]}=\\mathcal{R}^{[m_{r},n_{r}]}[\\mathsf{G}^{[n_{g}]}]$ built from a nonderived $(m_{r},n_{r})$-ring and a nonderived $n_{g}$-ary group. A central result is the derivation of the \"quantization\" conditions that interrela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.14029","kind":"arxiv","version":2},"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/2510.14029/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"}