{
  "abstract": "The notion of gap-richness was recently introduced to quantify the ability to open spectral gaps for periodic word models by arbitrarily small perturbations and is useful in the construction of almost-periodic operators having exotic spectral properties, such as Cantor spectrum of zero Hausdorff dimension. Given a subset of Euclidean space that is locally dense in the Zariski topology, we show that any image of such a set under a nonconstant polynomial is gap-rich. This generalizes the scope of previous work in several ways, including allowing local correlations into potential blocks and allowing for totally disconnected sets of realizations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21029",
  "author_total": 2,
  "authors": [
    {
      "name": "Jake Fillman"
    },
    {
      "name": "Yi-Sheng Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7p2s66w1hzmtj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21029",
  "fulltext_url": null,
  "id": "7p2s66w1hzmtj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21029",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213954679",
  "pdf_url": "https://arxiv.org/pdf/2609.21029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7p2s66w1hzmtj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the identification of certain classes of gap-rich sets",
  "title_text": "On the identification of certain classes of gap-rich sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/7p2s66w1hzmtj",
  "venue": "arXiv",
  "versions": []
}