{
  "abstract": "Local inference for spatial point distributions is dominated by Monte Carlo calibration. We develop an alternative based on the Tweedie--Miyasawa identities of empirical Bayes, which relate locally weighted moments of a point distribution under a Gaussian kernel to derivatives of its log-intensity in scale space. We first establish a rigidity theorem showing that the structure of these identities forces the Gaussian kernel. Under complete spatial randomness, we derive a closed-form null distribution for a bounded inter-scale contrast, yielding a calibrated simulation-free pointwise test. In experiments, the measured type I error is 0.070 at a nominal level of 0.05, with a calibration cost 199 times smaller than Monte Carlo for the same local statistic. We then derive a contamination law for structures of dimension m and width w embedded in a uniform background, together with an explicit detectability threshold. For a filament in three dimensions, the threshold is 16 pi. The resulting scale-resolved local dimension estimator has no free parameters. Applications to California seismicity, a trefoil knot, and 10,071 SDSS galaxies show that the method separates local structures across scales without a spatial mesh and reproduces published cosmic web fractions. All experiments are reproducible from a single public script.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16497",
  "author_total": 2,
  "authors": [
    {
      "name": "Henock Mwanza Lubukayi"
    },
    {
      "name": "Mechack Kabanga Ntolo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4syypraxq6wp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16497",
  "fulltext_url": null,
  "id": "d4syypraxq6wp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16497",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7213391730",
  "pdf_url": "https://arxiv.org/pdf/2609.16497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4syypraxq6wp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Locally calibrated and mesh-free inference for spatial point distributions: closed-form null, contamination law, and detectability threshold",
  "title_text": "Locally calibrated and mesh-free inference for spatial point distributions: closed-form null, contamination law, and detectability threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:51Z",
  "url": "https://research.draconitic.com/paper/d4syypraxq6wp",
  "venue": "arXiv",
  "versions": []
}