{
  "abstract": "The single-seed Rule 30 cone has unbounded least diagonal periods in both directions. On the finite-support side, first contact fixes the least Newton index and an integer polynomial lift gives a Fibonacci ceiling. For reflected Rule 86, a backward map on periodic tail profiles retains the zero boundary and bounds periods independently of transients. At depth $m$, the Rule 30 period is at least $\\lfloor m/2\\rfloor+1$; for natural Rule 86 cuts through depth $m$, the largest period is at least $\\tfrac12\\log_2(m+2)$. This proves infinitely many reset/integration period doublings. The physical Rule 135 orbit is a translated complement of Rule 30 after its first step, yielding finite or cofinite supports. A separately initialized auxiliary recurrence has exact index-by-index stabilization. Residue tables and block formulas describe the remaining structure and permit evaluation from supplied representations. Construction and minimization remain separate costs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25077",
  "author_total": 1,
  "authors": [
    {
      "name": "Tigran Nersissian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0nngk3mr1kaag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25077",
  "fulltext_url": null,
  "id": "0nngk3mr1kaag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25077",
  "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",
      "nlin.CG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0nngk3mr1kaag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25077"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Diagonal Periods and Newton Supports of Rules 30, 86 and 135",
  "title_text": "Diagonal Periods and Newton Supports of Rules 30, 86 and 135",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/0nngk3mr1kaag",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.5281/zenodo.22747716",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}