{
  "first_figure": {
    "domain": "(0,1)",
    "point_formula": "x_j=1-2^(-j)",
    "mass_formula": "w_j=2^(j^2)",
    "radius_formula": "epsilon_j=2^(-j^2-2j-8)",
    "error_bound_formula": "w_j*epsilon_j=2^(-2j-8)",
    "infinite_sum_exact": "1/768",
    "sampled_indices": [
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "samples": [
      {
        "j": 1,
        "log2_mass": 1,
        "log2_radius": -11,
        "log2_error_bound": -10
      },
      {
        "j": 2,
        "log2_mass": 4,
        "log2_radius": -16,
        "log2_error_bound": -12
      },
      {
        "j": 3,
        "log2_mass": 9,
        "log2_radius": -23,
        "log2_error_bound": -14
      },
      {
        "j": 4,
        "log2_mass": 16,
        "log2_radius": -32,
        "log2_error_bound": -16
      },
      {
        "j": 5,
        "log2_mass": 25,
        "log2_radius": -43,
        "log2_error_bound": -18
      },
      {
        "j": 6,
        "log2_mass": 36,
        "log2_radius": -56,
        "log2_error_bound": -20
      }
    ],
    "plots_are_not_Dirac_height_graphs": true,
    "proof_locators": [
      "formal Lemma1.1",
      "learner Example1",
      "learner Exercise1"
    ]
  },
  "second_figure": {
    "domain": "(0,1)",
    "point_formula": "x_j=1-2^(-j)",
    "datum_formula": "sum partial^j delta_(x_j)",
    "primitive_formula": "sum partial^(j-1) delta_(x_j)",
    "equation": "partial_t u=f",
    "excluded_endpoint": 1,
    "samples": [
      {
        "j": 1,
        "x_j": 0.5,
        "datum_order": 1,
        "primitive_order": 0
      },
      {
        "j": 2,
        "x_j": 0.75,
        "datum_order": 2,
        "primitive_order": 1
      },
      {
        "j": 3,
        "x_j": 0.875,
        "datum_order": 3,
        "primitive_order": 2
      },
      {
        "j": 4,
        "x_j": 0.9375,
        "datum_order": 4,
        "primitive_order": 3
      },
      {
        "j": 5,
        "x_j": 0.96875,
        "datum_order": 5,
        "primitive_order": 4
      },
      {
        "j": 6,
        "x_j": 0.984375,
        "datum_order": 6,
        "primitive_order": 5
      }
    ],
    "orders_unbounded_in_both_complete_series": true,
    "proof_locators": [
      "formal Theorem4.1",
      "formal Theorem5.1",
      "learner Example2",
      "learner Exercises3–4"
    ]
  }
}