{
  "annotation_id": "af5384a8-9562-4f1e-bfbb-8577d90ae6f4",
  "date_created": "2026-03-02T18:01:31.941000Z",
  "date_modified": "2026-03-02T18:01:31.941000Z",
  "file_hash": "9dea0705d208d131a444430eac038c234681eb4f600c36b0b7d232b2e53b17a5",
  "private": false,
  "record": {
    "abstract": "Faced with a sequence of N binary events, such as coin flips (or Ising\nspins), it is natural to ask whether these events reflect some underlying\ndynamic signals or are just random. Plausible models for the dynamics of hidden\nbiases lead to surprisingly high probabilities of misidentifying random\nsequences as biased. In particular, this probability decays as N^(-1/4), so\nthat no reasonable amount of data would be sufficient to induce the concept of\na fair coin with high probability. I suggest that these theoretical results may\nbe relevant to understanding experiments on the apparent misperception of\nrandom sequences by human observers.",
    "arxiv_id": "q-bio/0508044",
    "authors": [
      "William Bialek"
    ],
    "categories": [
      "q-bio.NC",
      "q-bio.QM"
    ],
    "title": "Should you believe that this coin is fair?",
    "url": "https://arxiv.org/abs/q-bio/0508044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "942b471f-5f21-45aa-8a3b-f906912970a0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}