{
  "abstract": "A local deterministic model can reproduce Bell-inequality violations only if the hidden state depends on the measurement settings. Hall found the minimum such dependence for the singlet state [Phys. Rev. Lett. 105, 250404 (2010)] and posed the corresponding problem for the Mermin state [Phys. Rev. A 84, 022102 (2011)]. This paper solves it, for the $n$-party GHZ-Mermin scenario at every $n \\geq 3$, with the marginals reproduced as well as the correlators. The minimum measurement-dependence fraction is $F_{\\min}(n) = R/[2(R+1)]$, with $R = 2^{\\lfloor (n-1)/2 \\rfloor}$ the Mermin violation ratio: $1/3, 2/5, 4/9, 8/17, \\ldots$, always below $1/2$. The lower bound follows from Mermin's inequality by a general overlap bound; the upper bound is an explicit model, uniform on the hidden-variable classes that violate the fewest constraints, with closed-form counts; a reduction theorem shows that for Mermin scenarios the marginals impose no additional dependence. The Mermin values are also certified by integer-arithmetic enumeration through $n = 22$. The formula was stated as a conjecture in the first version of this paper and was first proved, by a different route, by Wang, Yao and Chen; the proof here was obtained independently and the two agree. Every minimal contradiction of size $k$ among stabilizer constraints has correlator-only minimum $1/(k-1)$. With the marginals included the minimum is the same on every core of the $C_5$ ring cluster, on the size-4 and size-5 cores of $C_4$ and on every four-core of $C_6$, but larger on the size-6 and size-7 cores of $C_4$ and on 112 of the 1,920 five-cores of $C_6$, with exact certificates on both sides in every case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.00124",
  "author_total": 1,
  "authors": [
    {
      "name": "Aaron Alai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apmmtp775hrdj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.00124",
  "fulltext_url": null,
  "id": "apmmtp775hrdj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.00124",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7172438727",
  "pdf_url": "https://arxiv.org/pdf/2608.00124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apmmtp775hrdj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2608.00124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.00124"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations",
  "title_text": "Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:18Z",
  "url": "https://research.draconitic.com/paper/apmmtp775hrdj",
  "venue": "arXiv",
  "versions": []
}