{
  "article_slug": "ensemble-epistemic-correlation",
  "figures": [
    {
      "id": "correlation-floor",
      "kind": "analytical_curve",
      "caption": "Exact author-constructed equicorrelated scalar error variance with individual variance one; nonnegative rho is valid for all displayed M. No trained-network measurements.",
      "x": {
        "name": "Ensemble members M",
        "values": [
          1,
          2,
          4,
          8,
          16,
          32
        ]
      },
      "series": [
        {
          "name": "rho=0.0",
          "values": [
            1.0,
            0.5,
            0.25,
            0.125,
            0.0625,
            0.03125
          ]
        },
        {
          "name": "rho=0.2",
          "values": [
            1.0,
            0.6000000000000001,
            0.4,
            0.30000000000000004,
            0.25,
            0.225
          ]
        },
        {
          "name": "rho=0.8",
          "values": [
            1.0,
            0.9,
            0.8500000000000001,
            0.8250000000000001,
            0.8125,
            0.80625
          ]
        }
      ]
    },
    {
      "id": "shared-bias-risk",
      "kind": "analytical_curve",
      "caption": "Exact author-constructed expected squared error, shared bias .5 and individual zero-mean error variance one. No classification or OOD detector scores are inferred.",
      "x": {
        "name": "Ensemble members M",
        "values": [
          1,
          2,
          4,
          8,
          16,
          32
        ]
      },
      "series": [
        {
          "name": "Bias-squared contribution",
          "values": [
            0.25,
            0.25,
            0.25,
            0.25,
            0.25,
            0.25
          ]
        },
        {
          "name": "Total MSE, rho=0.0",
          "values": [
            1.25,
            0.75,
            0.5,
            0.375,
            0.3125,
            0.28125
          ]
        },
        {
          "name": "Total MSE, rho=0.2",
          "values": [
            1.25,
            0.8500000000000001,
            0.65,
            0.55,
            0.5,
            0.47500000000000003
          ]
        },
        {
          "name": "Total MSE, rho=0.8",
          "values": [
            1.25,
            1.15,
            1.1,
            1.075,
            1.0625,
            1.0562500000000001
          ]
        }
      ]
    }
  ],
  "cover_prompt": "Premium scientific editorial cover, landscape 3:2, no words. Several distinct jade optical prisms cast golden beams toward a shared focal point; some beams overlap perfectly in a single dark emerald shadow while a few reveal separate fine paths. Warm ivory stone laboratory sculpture, subtle brass rings, precise luminous geometry, restrained visual metaphor for shared error and complementary viewpoints. No fake data plots, no eyes or robots.",
  "numeric_data_provenance": "Computed and checked by the corresponding standalone standard-library script; constructed, not empirical."
}