{
  "article_slug": "pac-bayes-prior-dependence",
  "figures": [
    {
      "id": "sample-prior",
      "kind": "analytical_curve",
      "caption": "Author-constructed fixed-prior certificate arithmetic: zero empirical stochastic loss, delta=.05, KL log4 or log100. No actual trained network is certified.",
      "x": {
        "name": "Certification sample size n",
        "values": [
          20,
          50,
          100,
          500,
          1000
        ]
      },
      "series": [
        {
          "name": "KL=log4 upper risk",
          "values": [
            0.28010650217486266,
            0.1311838198016152,
            0.07112173646419762,
            0.016231777316818685,
            0.00849278228249184
          ]
        },
        {
          "name": "KL=log100 upper risk",
          "values": [
            0.3871259253383309,
            0.1853536797845975,
            0.10054508337476264,
            0.022544690528610856,
            0.01167918981945082
          ]
        }
      ]
    },
    {
      "id": "selection-cost",
      "kind": "analytical_curve",
      "caption": "Author-constructed n=100, zero empirical stochastic loss, delta=.05, base KL log4. Simultaneous confidence over M independently prespecified priors adds log M; plotted series are upper risks, not adaptive-prior certificates.",
      "x": {
        "name": "Prespecified prior count M",
        "values": [
          1,
          2,
          4,
          16,
          64,
          256
        ]
      },
      "series": [
        {
          "name": "Valid family-selection upper risk",
          "values": [
            0.07112173646419762,
            0.07753796730800933,
            0.08390987800799043,
            0.09652196142816905,
            0.10896041056894767,
            0.12122761590476094
          ]
        },
        {
          "name": "One prespecified prior upper risk",
          "values": [
            0.07112173646419762,
            0.07112173646419762,
            0.07112173646419762,
            0.07112173646419762,
            0.07112173646419762,
            0.07112173646419762
          ]
        }
      ]
    }
  ],
  "cover_prompt": "Premium scientific editorial cover, landscape 3:2, no words. A precise brass balance holds a luminous jade hypothesis crystal on one side and a stack of thin translucent ivory evidence sheets on the other; multiple faint candidate crystals sit behind a closed golden reference frame, only one admitted by a visible narrow gate. Dark emerald stone, warm cream light, elegant mathematical restraint. Conceptual illustration of prior commitment and information accounting; no numbers or fake experimental charts.",
  "numeric_data_provenance": "Computed and checked by the corresponding standalone standard-library script; constructed, not empirical."
}