{
  "abstract": "I prove that all Mellin residues are determined exactly by integer samples known up to errors smaller than every algebraic order, for an explicit class of functions consisting of a slow component with a complete inverse-power expansion and countably many carriers $\\exp(2πiσ2^k a^x)$ with admissible envelopes. A single exceptional null set of parameters $a>1$ works for the entire function class. The key estimate is an eventual uniform lower bound for a polynomially weighted sampling Gram matrix on windows of length $N^{1/2}$, with $O(N^{1/4})$ active modes. I derive this bound from parameter-averaged oscillatory integrals and a finite trace-moment comparison with product Haar measure, retaining the exact resonances among dyadic frequencies. Summed Taylor estimates then identify every coefficient of the slow asymptotic expansion, and a Mellin continuation argument identifies these coefficients with the actual residues. I also give an alternative derivation from existing higher-correlation estimates, an infinite-mode example, and exact counterexamples at integer parameters. The result supplies an interpolation-invariance statement for a model class motivated by Mellin averaging in quantum gravity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38234",
  "author_total": 1,
  "authors": [
    {
      "name": "Yifan He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v74ep7xxwc2q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38234",
  "fulltext_url": null,
  "id": "2v74ep7xxwc2q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38234",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7215083790",
  "pdf_url": "https://arxiv.org/pdf/2609.38234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v74ep7xxwc2q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.38234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Integer Sampling and the Identifiability of Mellin Residues",
  "title_text": "Integer Sampling and the Identifiability of Mellin Residues",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/2v74ep7xxwc2q",
  "venue": "arXiv",
  "versions": []
}