{
  "abstract": "Under local magnetic Gauss constraints, vertex-disjoint regions can have commuting physical observable algebras that do not generate all observables on their union. We construct such counterexamples for every finite non-Abelian group on regular square tori, retaining the full magnetic physical space and original supports inside a fixed contractible disk. A peripheral projector selects inputs on which a joint transition preserves the constraints, while its loop factor alone fails the universal test over physical exterior completions. For a specified support family around a fixed eight-edge square loop, additivity fails if and only if the group is non-Abelian and each inner face is covered by at least one of its two prescribed peripheral edges. Leaving a face uncovered restores full additivity. For the same loop, additivity also holds with any region at vertex-set graph distance at least two. These results refute a recent group-double additivity proposition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25329",
  "author_total": 1,
  "authors": [
    {
      "name": "Yi Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wsaxwsev1pfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25329",
  "fulltext_url": null,
  "id": "4wsaxwsev1pfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25329",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223058921",
  "pdf_url": "https://arxiv.org/pdf/2610.25329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wsaxwsev1pfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25329"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Failure of disjoint additivity under magnetic Gauss constraints",
  "title_text": "Failure of disjoint additivity under magnetic Gauss constraints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/4wsaxwsev1pfa",
  "venue": "arXiv",
  "versions": []
}