{
  "abstract": "In this paper, we study the graph shotgun assembly problem in the labeled lattice model, as introduced by Mossel and Ross (2019). We start with a $d$-dimensional lattice of length $n$, where the color of each vertex is sampled i.i.d. from a distribution $π$. Then, we ask whether it is possible to reconstruct the coloring of the lattice given the coloring of each subgrid of length $k$. While previous work by Ding and Liu (2023) and Demidovich, Panichkin, and Zhukovskii (2023) identified the reconstruction threshold when $π$ is uniform, we examine the non-uniform case. This paper establishes a sufficient condition for the impossibility of reconstruction for $d \\geq 2$ using information-theoretic arguments. Our negative result matches the known threshold in the uniform case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05532",
  "author_total": 3,
  "authors": [
    {
      "name": "Julia Gaudio"
    },
    {
      "name": "Charlie K. Guan"
    },
    {
      "name": "Andrew Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8thscvxr17vc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05532",
  "fulltext_url": null,
  "id": "d8thscvxr17vc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05532",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8thscvxr17vc.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Shotgun Assembly of the Non-Uniform Labeled Lattice Model",
  "title_text": "Shotgun Assembly of the Non-Uniform Labeled Lattice Model",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/d8thscvxr17vc",
  "venue": "arXiv",
  "versions": []
}