{
  "article_slug": "self-distillation-teacher-dynamics",
  "figures": [
    {
      "id": "teacher-step",
      "kind": "analytical_curve",
      "caption": "Exact author-constructed scalar step response q_t=1−beta^t with q0=0; no neural training convergence claim.",
      "x": {
        "name": "Update steps t",
        "values": [
          0,
          1,
          2,
          5,
          10,
          20,
          50,
          100
        ]
      },
      "series": [
        {
          "name": "beta=0.5",
          "values": [
            0.0,
            0.5,
            0.75,
            0.96875,
            0.9990234375,
            0.9999990463256836,
            0.9999999999999991,
            1.0
          ]
        },
        {
          "name": "beta=0.9",
          "values": [
            0.0,
            0.09999999999999998,
            0.18999999999999995,
            0.40950999999999993,
            0.6513215599,
            0.8784233454094307,
            0.9948462247926799,
            0.9999734386011124
          ]
        },
        {
          "name": "beta=0.99",
          "values": [
            0.0,
            0.010000000000000009,
            0.01990000000000003,
            0.04900995010000009,
            0.09561792499119559,
            0.18209306240276923,
            0.39499393286246365,
            0.6339676587267709
          ]
        }
      ]
    },
    {
      "id": "variance-lag",
      "kind": "analytical_curve",
      "caption": "Exact author-constructed stationary scalar noise variance factors. Independent temporal noise is reduced by (1−beta)/(1+beta); perfectly shared noise is not reduced. Mean delays beta/(1−beta) are printed in the verification output, not mixed into this variance axis.",
      "x": {
        "name": "Averaging beta",
        "values": [
          0,
          0.5,
          0.8,
          0.9,
          0.95,
          0.99
        ]
      },
      "series": [
        {
          "name": "Independent-noise variance factor",
          "values": [
            1.0,
            0.3333333333333333,
            0.11111111111111108,
            0.05263157894736841,
            0.025641025641025664,
            0.005025125628140708
          ]
        },
        {
          "name": "Perfectly correlated-noise variance factor",
          "values": [
            1.0,
            1.0,
            1.0,
            1.0,
            1.0,
            1.0
          ]
        }
      ]
    }
  ],
  "cover_prompt": "Premium scientific editorial cover, landscape 3:2, no words. Two related translucent jade sculptures face each other across a warm ivory plane; one sharp golden trajectory advances while a softer layered ribbon follows with a visible gentle delay, preserving traces of earlier positions. Fine brass temporal rings, deep emerald shadows, restrained cinematic light. Conceptual moving-teacher self-distillation, not literal human figures or a measured chart.",
  "numeric_data_provenance": "Computed and checked by the corresponding standalone standard-library script; constructed, not empirical."
}