{
  "abstract": "In symbolic dynamics, the fixed-point construction from [DRS12] defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a \"black box\" abstraction of this method phrased in terms of substitutions and S-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.",
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  "article_type": null,
  "arxiv": "2609.28207",
  "author_total": 4,
  "authors": [
    {
      "name": "Antonin Callard"
    },
    {
      "name": "Pierre Guillon"
    },
    {
      "name": "Léo Paviet Salomon"
    },
    {
      "name": "Pascal Vanier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/916fj2fhd6gp6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28207",
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  "id": "916fj2fhd6gp6",
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  "landing_url": "https://hal.science/hal-05761449v1",
  "language": "en",
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  "pdf_url": "https://hal.science/hal-05761449/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/916fj2fhd6gp6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:39Z",
      "native_id": "hal-05761449",
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      "url": "https://hal.science/hal-05761449v1"
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    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28207"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces",
  "title_text": "Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/916fj2fhd6gp6",
  "venue": "HAL",
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}