{
  "annotation_id": "a580964f-c0aa-480c-a8ce-79690af43f2b",
  "date_created": "2026-02-17T05:53:20.113000Z",
  "date_modified": "2026-02-17T05:53:20.113000Z",
  "file_hash": "48eb380f3619711a54e85f980eca72a0f2211eb95d1e5b5834331fc184d0112b",
  "private": false,
  "record": {
    "abstract": "We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice\u0027\u0027) loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature\u0027s hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations.",
    "arxiv_id": "2601.09339",
    "authors": [
      "Takara Nomura",
      "Koichi Yamagata",
      "Akio Fujiwara"
    ],
    "categories": [
      "quant-ph",
      "cs.GT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A game-theoretic probability approach to loopholes in CHSH experiments",
    "url": "https://arxiv.org/abs/2601.09339",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ae9b26ab-9ef8-4329-901c-0cc204c34dbb",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}