{
  "abstract": "We study the cost of certifying a scalar target driven by a product of centered Bernoulli means when an unobserved terminal gate leaves irreducible uncertainty. Each factor can be queried independently at a price. We derive the exact identified interval and determine when a requested accuracy is feasible. At every fixed strictly feasible interior instance, the optimal high-confidence expected cost is $(1+o(1))\\log(1/δ)/D^*$, where $D^*$ is an answer-and-allocation information game; a globally honest procedure attains this benchmark. At product cancellation, we solve the game through a one-dimensional inverse-KL equation and explicit cost weights. For two tickets, quartic projections and rational bounds give checkable global optimality gaps. Joint confidence--precision limits expose a failure of the analyzed fixed pilot: it can cost asymptotically at least twice the optimum. A charged, precision-aware pilot with checkpoint certification restores optimal expected cost in exact arithmetic when $\\log\\{e+\\log(1/g)\\}=o(\\log(1/δ))$ for effective precision $g$, including exponential and certain double-exponential precision scales. Pooled rescue preserves validity and cannot increase observation cost on coupled paths. Implemented auditors verify returns by rational inequalities; reproducible experiments show both savings and finite-confidence overhead. These guarantees concern the specified independent-reference model and its scalar target.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07567",
  "author_total": 3,
  "authors": [
    {
      "name": "Abdallah Skiredj"
    },
    {
      "name": "Abderrahman Skiredj"
    },
    {
      "name": "Amal El Fallah Seghrouchni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03efsdxjd5yq6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07567",
  "fulltext_url": null,
  "id": "03efsdxjd5yq6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07567",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07567",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03efsdxjd5yq6.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07567",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07567"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling",
  "title_text": "Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:27Z",
  "url": "https://research.draconitic.com/paper/03efsdxjd5yq6",
  "venue": "arXiv",
  "versions": []
}