{
  "abstract": "In this article, we first investigate the box dimension results for the graphs of continuous functions defined on $\\mathfrak{F\\times F}$, where $\\mathfrak{F}$ is the self-similar fractal generated by an iterated function system (IFS) exhibiting the open set condition (OSC). Following this, we manifest the existence of a prevalent surface, defined by a continuous function on $\\mathfrak{F\\times F}$, that satisfies the horizon property in relation to the box dimension, i.e., the box dimension of the prevalent surface is greater than that of its horizon up to a constant $η$, where $η$ is the box dimension of the self-similar fractal $\\mathfrak{F}$. Finally, we provide an example consolidating that the OSC on the underlying IFS of $\\mathfrak{F}$ cannot be dropped.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.21047",
  "author_total": 3,
  "authors": [
    {
      "name": "Gurubachan"
    },
    {
      "name": "S. Verma"
    },
    {
      "name": "V. V. M. S. Chandramouli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vsencrvhwg6n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.21047",
  "fulltext_url": null,
  "id": "0vsencrvhwg6n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.21047",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7204071805",
  "pdf_url": "https://arxiv.org/pdf/2608.21047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vsencrvhwg6n.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:13Z",
      "native_id": "2608.21047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.21047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the horizon problem over the product of self-similar fractals",
  "title_text": "On the horizon problem over the product of self-similar fractals",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0vsencrvhwg6n",
  "venue": "arXiv",
  "versions": []
}