{
  "abstract": "Signals that predict whether a chain-of-thought (CoT) trace is correct are compared by AUC, but deploying one requires a threshold with a guarantee. We ask what distribution-free selective guarantees deliver for CoT verifiers at realistic calibration budgets of tens to a few hundred labelled problems, using seven open models, five verifier signals and 37,000 graded traces. The central observation is validity by abstention: an $(α,δ)$-valid procedure that issues a certificate with probability $P_{\\rm fire}$ bounds the failure probability of an issued certificate only by $δ/P_{\\rm fire}$, so a certificate that rarely fires can be valid and wrong every time it is used. In a simulation with known risk the standard certificate fails in at most 0.3% of calibration draws but in up to 69% of those in which it fires. A certification floor and a lattice condition for Benjamini-Hochberg conformal selection explain why certificates abstain at these budgets, and the data bear them out: the standard certificate returns nothing or a large accepted set, and an unreadable residual-stream probe buys two to three times the coverage of the readable signals, an edge a cross-fitted reconstruction cannot recover linearly from the readable features. We then give a floor-started fixed-sequence certificate, valid without monotonicity assumptions, that covers more than the Bonferroni certificate on every model-signal pair and raises coverage at the non-vacuous target $0.75π_0$ from 0.05 to 0.16, although the floor keeps absolute coverage small. Finally, a certificate cannot see what matters after deployment: under benchmark shift the error among accepted traces tracks the new task's base error, and under best-of-$n$ selection against the verifier it rises past the target while the empirical failure frequency stays below $δ$, because abstention absorbs the failures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09541",
  "author_total": 1,
  "authors": [
    {
      "name": "Arjun Balaji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50g8mz68jn2jh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09541",
  "fulltext_url": null,
  "id": "50g8mz68jn2jh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09541",
  "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.CL"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Explainable Artificial Intelligence (XAI)"
    ]
  ],
  "openalex": "W7220958569",
  "pdf_url": "https://arxiv.org/pdf/2610.09541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50g8mz68jn2jh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:48Z",
      "native_id": "2610.09541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Certified by Abstention: Distribution-Free Guarantees for Chain-of-Thought Verifiers at Small Calibration Budgets",
  "title_text": "Certified by Abstention: Distribution-Free Guarantees for Chain-of-Thought Verifiers at Small Calibration Budgets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:48Z",
  "url": "https://research.draconitic.com/paper/50g8mz68jn2jh",
  "venue": "arXiv",
  "versions": []
}