{
  "abstract": "A latent severity has a bounded lower tail with density of shape alpha and scale L. It is observed only through a fixed Markov kernel K that is biased and non-additive. The relative conditional spread of K diverges at the endpoint. Our sample is i.i.d. from the marginal Q alone, with no anchoring covariate or instrument. We prove a dichotomy. The shape index alpha is identifiable: for every admissible choice of the class constants, any two observationally equivalent members of a lean class share alpha, determined by a near-endpoint expansion of Q. The rate, namely L and the fixed-scale exceedance p_tau, does not survive. There exist admissible shared class constants and two members of a smaller regularity class whose observed laws coincide exactly. Across the pair alpha agrees, whereas L and p_tau move. A degenerate Le Cam two-point bound excludes any uniformly consistent estimator of either, and pointwise consistency fails at one member. Only the rate needs an anchor. We conjecture that a known kernel family with known edge map identifies the rate fiber by fiber if and only if the family satisfies a fixed-scale injectivity clause, and we prove the sufficiency direction. In surrogate safety, uncalibrated conflict data give the shape of near-crash risk, not its absolute rate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27384",
  "author_total": 1,
  "authors": [
    {
      "name": "Jiarui Qi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8q52stzhahpra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27384",
  "fulltext_url": null,
  "id": "8q52stzhahpra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27384",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7214405959",
  "pdf_url": "https://arxiv.org/pdf/2609.27384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8q52stzhahpra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2609.27384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Shape without scale: an identifiability dichotomy for a bounded tail observed through a non-additive measurement kernel",
  "title_text": "Shape without scale: an identifiability dichotomy for a bounded tail observed through a non-additive measurement kernel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/8q52stzhahpra",
  "venue": "arXiv",
  "versions": []
}