{
  "abstract": "We study internal exact controllability of the free Schrödinger equation on finite compact metric graphs with Kirchhoff conditions at interior vertices and a fixed Dirichlet-Neumann assignment at exterior vertices. For a prescribed primitive cycle or exterior-to-exterior path, we identify an arithmetic criterion ensuring that the corresponding scar is accessible by exact high-frequency eigenfunctions of a fixed target metric. The criterion is formulated by intersecting the regular scar stratum of the secular set with the orbit-closure torus of the target length vector, and it can hold for resonant metrics beyond the rationally independent class. Under an intrinsic Diophantine condition on the orbit-closure flow, the construction is quantitative: along an exact eigensequence the mass outside the prescribed support decays polynomially, yielding a polynomial degeneration law for finite-frequency observation when that support is uncontrolled. Rationally independent metrics have full phase-orbit closure and therefore make every primitive obstruction accessible. Combining this spectral result with the known graph-theoretic characterization and sufficiency of the Graph Geometric Control Condition (GGCC), we prove that, for every rationally independent and hence for Lebesgue-almost every metric, GGCC is necessary and sufficient for exact controllability at every positive time in the free setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09758",
  "author_total": 1,
  "authors": [
    {
      "name": "Binh T. Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mmnkvzpyyf0r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09758",
  "fulltext_url": null,
  "id": "9mmnkvzpyyf0r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09758",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7212176925",
  "pdf_url": "https://arxiv.org/pdf/2609.09758",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mmnkvzpyyf0r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09758",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09758"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Arithmetic Scar Accessibility and Generic Schrodinger Control on Metric Graphs",
  "title_text": "Arithmetic Scar Accessibility and Generic Schrodinger Control on Metric Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/9mmnkvzpyyf0r",
  "venue": "arXiv",
  "versions": []
}