{
  "abstract": "We show nonuniqueness for a discrete X-ray transform on $\\mathbb Z^2$ under quadratic decay. We construct an explicit nonzero function in $\\ell^1(\\mathbb Z^2)$ with pointwise decay $O(|z|^{-2})$ whose sums over integer lines vanish. We also obtain an infinite-dimensional null space with the same decay assumption. Furthermore, we show a result which indicates that the decay rate $|z|^{-2}$ may be sharp and faster decay may imply uniqueness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01294",
  "author_total": 2,
  "authors": [
    {
      "name": "Shubham R. Jathar"
    },
    {
      "name": "Jesse Railo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnrbveznq32hd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01294",
  "fulltext_url": null,
  "id": "bnrbveznq32hd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01294",
  "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.FA"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01294",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnrbveznq32hd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01294",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01294"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Counterexamples to uniqueness for a discrete X-ray transform under quadratic decay",
  "title_text": "Counterexamples to uniqueness for a discrete X-ray transform under quadratic decay",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bnrbveznq32hd",
  "venue": "arXiv",
  "versions": []
}