{
  "abstract": "Conformal test martingales (CTMs) are e-processes for sequentially testing exchangeability via p-values produced by a conformity function $A$. However, any distribution shift that preserves the push-forward $P\\circ A^{-1}$ leaves the p-value distribution invariant, rendering it invisible to every CTM based on $A$. We formalise this blind spot through the \\emph{$A$-equivalence class} $[P]_A$ and show that, for any target distribution $T$, there is a unique closest element $Q^\\ast\\in[P]_A$ in KL divergence---the \\emph{$A$-cryptic I-projection}---with explicit density $q^\\ast(z) = t(z)\\,p_S(A(z))/t_S(A(z))$ and a Pythagorean decomposition into detectable and cryptic components. When $A$ is the Neyman-Pearson likelihood ratio, the cryptic component vanishes, connecting our result to optimal e-value design. We demonstrate the theory on high-dimensional image data by empirically constructing this I-projection. By conditionally resampling EMNIST letters to identically match the conformity scores of MNIST digits, we demonstrate that a distribution can be shifted to a disjoint support while leaving the test martingale mathematically blinded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23131",
  "author_total": 1,
  "authors": [
    {
      "name": "Johan Hallberg Szabadváry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbn29akrebvwa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23131",
  "fulltext_url": null,
  "id": "bbn29akrebvwa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23131",
  "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.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7222981586",
  "pdf_url": "https://arxiv.org/pdf/2610.23131",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbn29akrebvwa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23131",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23131"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Information-Geometric Blind Spots of Conformal Test Martingales",
  "title_text": "Information-Geometric Blind Spots of Conformal Test Martingales",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/bbn29akrebvwa",
  "venue": "arXiv",
  "versions": []
}