{
  "formula_authority": "Exact formulas and proofs in the learner chapter",
  "first_figure": {
    "multiplier": "3^(-k)",
    "image_coordinates": "3^(-k)/sqrt(k)",
    "inverse_norm": "sqrt(sum_(k=1)^N 1/k)",
    "inverse_bounds": [
      "sqrt(log(N+1))",
      "sqrt(1+log(N))"
    ],
    "image_norm_squared": "log(9/8)",
    "image_error_upper_bound": "3^(-N)/sqrt(8(N+1))",
    "inverse_sample_range": [
      1,
      2000
    ],
    "error_bound_sample_range": [
      1,
      40
    ],
    "lower_panel_is_upper_bound_not_exact_error": true
  },
  "second_figure": {
    "rho": "c exp(-1/(1-16t^2)) for |t|<1/4;0 elsewhere",
    "normalization_c": "9.0091344841743240419991250222393229202967817531550668106948811774",
    "decimal_precision_for_normalization": 65,
    "psi": "rho(x-1/2)-rho(x+1/2)",
    "phi": "-integral_(-infinity)^x psi(t)dt",
    "negative_bump_mass": -1,
    "positive_bump_mass": 1,
    "support_bounds": [
      "-3/4",
      "3/4"
    ],
    "exact_plateau": {
      "interval": [
        "-1/4",
        "1/4"
      ],
      "value": 1
    },
    "adjoint_sign": "-D phi=psi",
    "sample_count": 8193,
    "drawing_integral_method": "Composite trapezoid for numerical samples",
    "sampled_plateau_max_error": 6.661338147750939e-16,
    "curves_are_numerical_samples_not_a_proof": true
  }
}