{
  "abstract": "What can a finished text reveal about the process that produced it? Drawing on Turing's imitation game and statistical decision theory, this article examines the limits of AI-text detection as an inference from a completed object to an unobserved history. For two known source distributions with equal prior probabilities, a standard identity gives the minimum average classification error as half their probability overlap. This overlap is one minus their total variation distance. Perfect detection therefore requires nonoverlapping distributions; useful discrimination does not. In practice, the problem is harder: human and machine writing form changing families of distributions, posterior probabilities depend on base rates, and ``AI-written'' becomes ambiguous when people and software contribute to the same text. Turing's interrogator can ask another question; a detector restricted to finished prose cannot. Distinguishability, source attribution, authentication, and compliance are different inferential tasks. The paper's own documented human-AI provenance shows what a production history can reveal that a binary label cannot.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13660",
  "author_total": 1,
  "authors": [
    {
      "name": "Santiago Schnell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4kx909ydaw5tf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13660",
  "fulltext_url": null,
  "id": "4kx909ydaw5tf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13660",
  "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.HO"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Authorship Attribution and Profiling"
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  "openalex": "W7213354686",
  "pdf_url": "https://arxiv.org/pdf/2609.13660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4kx909ydaw5tf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Who Wrote This? Turing, Total Variation, and the Mathematics of AI-Text Detection",
  "title_text": "Who Wrote This? Turing, Total Variation, and the Mathematics of AI-Text Detection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/4kx909ydaw5tf",
  "venue": "arXiv",
  "versions": []
}