{
  "abstract": "Place closed Euclidean balls of radius r at the points of (1/2, 1/2, ..., 1/2) + Z^n. The view-obstruction problem for spheres asks for the least r such that every ray from the origin into the open positive orthant meets a ball. Equivalently, it asks for D_n = sup_v min_{t in R} sum_i ||t v_i - 1/2||{Z}^2 over positive integer vectors v, where ||x||{Z} denotes the distance from x to the nearest integer. The values for n <= 5 are classical. We prove D_6 = 107/312, attained only by permutations of (12, 9, 7, 5, 3, 2), and D_7 = 73/180, attained only by permutations of (11, 10, 8, 7, 4, 3, 1). The proof reduces the supremum to a finite search. The key facts are an exact lower bound d_n(v) >= delta^2_U for every rational subspace U perpendicular to v, a matching fiber upper bound, and Banaszczyk's transference theorem, applied along the Korkine-Zolotarev flag of the dual lattice v^perpendicular intersection Z^n. The search is quotiented by signed coordinate permutations and carried out entirely in exact rational arithmetic. It terminates with a certificate: no node of the search is left unresolved, and every surviving candidate is evaluated exactly. The method also recovers the known values for n = 3, 4, 5.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37711",
  "author_total": 1,
  "authors": [
    {
      "name": "Vineet Kahlon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a9chgy4jvfe7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37711",
  "fulltext_url": null,
  "id": "4a9chgy4jvfe7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37711",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a9chgy4jvfe7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The View-Obstruction Problem for Spheres in Dimensions Six and Seven",
  "title_text": "The View-Obstruction Problem for Spheres in Dimensions Six and Seven",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/4a9chgy4jvfe7",
  "venue": "arXiv",
  "versions": []
}