{
  "abstract": "We establish a uniform pole-subtracted limiting absorption principle for a fixed cluster of \\(N\\) disjoint three-dimensional high-contrast elastic resonators when the contrast tends to infinity and \\(ω=δ^{1/2}τ\\) approaches the zero threshold. The exterior Dirichlet-to-Neumann map and a variational Grushin--Feshbach reduction give an exact decomposition of the cutoff resolvent into a uniformly bounded regular part and a finite-rank term governed by \\[ \\cM_δ^\\pm(ω) = δK-ω^2I_m \\mp\\iiδωΓ_0 +\\mathcal O(δ^2+δω^2). \\] The cutoff-resolvent norm is uniformly equivalent to \\(1+\\|(\\cM_δ^\\pm(ω))^{-1}\\|\\); hence the finite-dimensional channel carries every loss of uniformity. An elastic optical identity factors the leading radiation matrix through one total-force map into \\(\\C^3\\). Thus \\(\\rankΓ_0=3\\) and \\(\\dim\\KerΓ_0=6N-3\\). Compression to a static eigenspace of dimension \\(r\\) leaves at most three leading radiative channels. Simple bright poles have width \\(O(δ)\\), whereas force-dark poles with a positive second radiation form have width \\(O(δ^2)\\); the corresponding real-axis peaks have orders \\(δ^{-3/2}\\) and \\(δ^{-5/2}\\). We also treat multiple static eigenvalues, compute the spherical coefficients, and derive a conditional two-parameter crossover for a symmetry-broken dimer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09367",
  "author_total": 1,
  "authors": [
    {
      "name": "Yixian Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/at7q428a28m49.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09367",
  "fulltext_url": null,
  "id": "at7q428a28m49",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09367",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7202212665",
  "pdf_url": "https://arxiv.org/pdf/2608.09367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/at7q428a28m49.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2608.09367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09367"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Uniform Pole-Subtracted Limiting Absorption Principle for High-Contrast Elastic Resonator Clusters",
  "title_text": "A Uniform Pole-Subtracted Limiting Absorption Principle for High-Contrast Elastic Resonator Clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/at7q428a28m49",
  "venue": "arXiv",
  "versions": []
}