{
  "abstract": "Patient-reported pain location is diagnostically decisive for some presentations and nearly uninformative for others. A companion paper argues this is not one gradient of diagnostic utility but three distinct failures of localization. This paper gives those failures their mathematics and shows they are one object: a single Bayesian generative model failing at different nodes - the likelihood, the model class, and group- or context-dependence in that same likelihood. The count is not in dispute: the first three are failures of the inference that produces a felt location, and the fourth, added here, is a failure of reporting it. Anatomical multiplexing is a non-identifiable inverse problem: a rank-deficient referral matrix sends distinct causes to one report. Delocalized amplification is a change of generative model whose dynamics are a neural-field bifurcation, with spatial extent as the order parameter. Referred and atypical displacement is group- or context-dependence in the presentation likelihood - a probability, not a loss - whose consequence sits one layer downstream, in a decision threshold varying with group prevalence and cost. Repeated observation cannot reduce recoverable information about a fixed inferential target, an exact chain-rule identity, while practical value can fall. The fourth node is the report itself. A spatial Bayesian model factorizes mislocalization into referral blur, an anatomical offset and a precision-weighted cognitive override, and reproduces phantom-limb, mirror-box and central-post-stroke reports as regimes of one equation. It is estimable under conditions the paper states as necessary or sufficient rather than assuming them; Sec. 8 gives the design that meets them. One control is reported against the paper's own interest: the transport statistic first used to measure migration scores a stationary, spreading profile as though it had travelled.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00866",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Y. Shavit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adp0ngmx7040q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00866",
  "fulltext_url": null,
  "id": "adp0ngmx7040q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00866",
  "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",
      "q-bio.NC"
    ],
    [
      "arxiv",
      "stat.AP"
    ],
    [
      "openalex",
      "2703|Pain Management and Treatment"
    ]
  ],
  "openalex": "W7215979078",
  "pdf_url": "https://arxiv.org/pdf/2610.00866",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adp0ngmx7040q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:08Z",
      "native_id": "2610.00866",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00866"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "One Inference, Four Failure Modes: Formal Models of Why Pain Location Fails",
  "title_text": "One Inference, Four Failure Modes: Formal Models of Why Pain Location Fails",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:14Z",
  "url": "https://research.draconitic.com/paper/adp0ngmx7040q",
  "venue": "arXiv",
  "versions": []
}