{
  "abstract": "Let $S$ be a reachable image of a strongly connected synchronizing automaton and $\\varnothing\\ne A\\subsetneq S$. We determine the maximum shortest avoid-or-compress length over binary and arbitrary finite alphabets for $m=n-|S|=4$ and $m=5$. The exact values are $\\min(n-|A|,11)$ and $\\min(n-|A|,14)$, respectively. Uniform binary constructions attain both bounds. For the upper bounds, short-pair graphs and actual-image constraints reduce all parameters to finite necessary domains. Exhaustive checks exclude the domains, apart from a single relaxation eliminated by a multipartite overlap lemma. The largest calculation covers 3,206,988 domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39833",
  "author_total": 2,
  "authors": [
    {
      "name": "Qichao Wang"
    },
    {
      "name": "Daoyu Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/705zzd154yq3w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39833",
  "fulltext_url": null,
  "id": "705zzd154yq3w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39833",
  "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",
      "cs.FL"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/705zzd154yq3w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39833"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Exact Avoid-or-Compress Extrema for Dense Reachable Images: Defects Four and Five",
  "title_text": "Exact Avoid-or-Compress Extrema for Dense Reachable Images: Defects Four and Five",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/705zzd154yq3w",
  "venue": "arXiv",
  "versions": []
}