{
  "abstract": "For every integer $p\\ge2$, we construct a globally well-defined positive odd sequence $Q_p$ satisfying, after an explicit finite initial block, $Q_p(n)=Q_p(n-Q_p(n-1))+Q_p(n-Q_p(n-2))-(-1)^n$. Its binary block words admit the exact factorization $U_{p,k}=(A_k\\overline{A}_{k+1})^{p-1}A_{k+2}$, producing exactly $2p-1$ alternating signed arches per natural block. The elementary word heights converge uniformly to the Gaussian isoperimetric profile $φ\\circΦ^{-1}$. For each fixed $p$, this yields an explicit dyadic limiting profile with $2p-1$ sign transitions and a sharp relative-error constant $Λ_p=b_p/2$, where $b_p$ is determined by $b_p((3p-1)/2+Φ(-b_p))=φ(b_p)$. We determine all zeros and parity crossings in sufficiently large dyadic blocks. For $p\\ge3$, there are exactly $2p-1$ transverse even-index zeros, whereas the three-arch case $p=2$ exhibits an alternating four/six-zero pattern. An ordered frequency factorization gives exact dyadic histograms, moments, total-variation distances, and extremal multiplicities. The limiting frequency generating function $z^3/(2-z)$ is universal, although the highest finite multiplicities depend on $p$. Finally, the summatory function has main terms $N^2/4+(N/2)\\log_2N$, an explicit parameter-dependent log-periodic term of order $N$, and remainder $O_p(N/\\sqrt{\\log N})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01453",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Mantovanelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y2zejrr0sta6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01453",
  "fulltext_url": null,
  "id": "5y2zejrr0sta6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01453",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01453",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y2zejrr0sta6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01453",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01453"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Odd-Arch Family of Perturbed Hofstadter Q-Recursions: Gaussian Profiles and Exact Frequency Laws",
  "title_text": "An Odd-Arch Family of Perturbed Hofstadter Q-Recursions: Gaussian Profiles and Exact Frequency Laws",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5y2zejrr0sta6",
  "venue": "arXiv",
  "versions": []
}