{
  "schema": "AN02-entire-logarithm-geometry154/v1",
  "quadratic_example": {
    "complex_dimension": 1,
    "weight": "|z|^2",
    "centers": [
      -0.5,
      0.5
    ],
    "center_ball_radius": 0.25,
    "cutoff_inner_radius": "1/12",
    "cutoff_outer_radius": "1/6",
    "cutoff_definition": "h(1-t)/(h(1-t)+h(t)), t=(s-1/12)/(1/6-1/12), h(t)=exp(-1/t) if t>0 else 0",
    "exact_gap": "|z-a|^2",
    "actual_error_modulus": "0.5*abs(chi_prime(s))*exp(-N*s^2)",
    "plotted_N": [
      128,
      512,
      2048
    ],
    "positive_log_plot_floor": 1e-12,
    "returned_correction_plotted": false
  },
  "polynomial_example": {
    "f_N": "(1+z^N)/2",
    "target": "max(0,log|z|)",
    "zero_plot_degree": 13,
    "exact_zero_angles": "(2k+1)*pi/13, k=0,...,12",
    "highlighted_fixed_zero": [
      -1,
      0
    ],
    "error_plot_disk_radius": 2,
    "exact_L1_error": "pi*R^2*log(2)/N",
    "N_degrees": [
      1,
      64
    ],
    "quadrature_points": [
      1,
      3,
      13,
      32
    ],
    "pointwise_convergence_claimed_at_minus_one": false
  },
  "proof_locators": [
    "GD7\u2013GD9",
    "GD11"
  ],
  "human_source": "H\u00f6rmander II, Theorem 15.1.6 and Lemmas 15.1.7\u201315.1.8, pp. 277\u2013278"
}