{
  "abstract": "Query-conditioned probabilistic predictors answer logically related questions one at a time, and labels to check their calibration are often missing. For each restriction on what a bettor's stakes may use, a minimax theorem identifies, for finitely supported laws of the answers, the sharp label-free lower bound on the corresponding calibration residual. On bundles of different events its mean, marginal and joint stages can separate strictly, and a bundle's bound cannot be attributed to one question without assumptions on the others. The sharp marginal bound is discontinuous in the answers, and no label-free lower bound continuous in the Wasserstein distance stays within a constant factor of it. Lipschitz stakes give a stable bound, sharp for a smooth calibration residual and, for every positive Lipschitz constant, positive exactly when the sharp marginal bound is. On i.i.d. streams, projected online gradient ascent at fixed nodes gives fixed-horizon certificates whose shortfall is bounded by grid, learning and statistical terms, and predictable betting gives anytime-valid ones. In a preregistered study of four predictors on two data sets, all seven confirmatory certificates were positive (the eighth pair did not pass the pilot). A certificate shows only that calibration is at least this bad; zero means \"not refuted\".",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21567",
  "author_total": 1,
  "authors": [
    {
      "name": "Takahiro Kato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4mjn5hppk2dz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21567",
  "fulltext_url": null,
  "id": "a4mjn5hppk2dz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21567",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Machine Learning and Algorithms"
    ]
  ],
  "openalex": "W7222737224",
  "pdf_url": "https://arxiv.org/pdf/2610.21567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4mjn5hppk2dz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:00Z",
      "native_id": "2610.21567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Sharp and Stable Label-Free Calibration Certificates from Logical Coherence",
  "title_text": "Sharp and Stable Label-Free Calibration Certificates from Logical Coherence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/a4mjn5hppk2dz",
  "venue": "arXiv",
  "versions": []
}