{
  "schema": "AN02-compact-kernel-converse-figures/v1",
  "figure1": {
    "exact_graph": "z_L(xi)=xi+i L log(2+xi^2)",
    "scales": [
      12,
      14,
      16
    ],
    "kernel": "mu=delta_prime_0",
    "reciprocal": "q(z)=1/(i z)",
    "pole_set": [
      "0"
    ],
    "threshold": "Im z>2log(|z|+2)",
    "proof_locator": "manuscript Figure1 and learner Problem2",
    "exact_jacobian": "J=1+24i xi/(2+xi^2) at L12",
    "cutoff_R": 3,
    "cutoff_derivative_support": "3<=|xi|<=6",
    "real_samples": 1001,
    "real_interval": [
      -7,
      7
    ],
    "side_bound_locator": "manuscript5.8-5.11",
    "shading": "frequency projection of actual cutoff-derivative annuli; strip between endpoint graphs"
  },
  "figure2": {
    "exact_map": "z=(xi1+4i h,xi2+2i h), h=log(2+xi1^2+xi2^2)",
    "representation": "(xi1,xi2,lambda) with lambda=4h; Im z2=lambda/2 exactly",
    "exact_jacobian": "J=1+i(8xi1+4xi2)/(2+xi1^2+xi2^2)",
    "grid_samples_per_axis": 65,
    "real_axis_intervals": [
      [
        -3,
        3
      ],
      [
        -3,
        3
      ]
    ],
    "color": "Im J, not surface area or reciprocal estimate",
    "cone": "Gamma={theta1>|theta2|}",
    "exact_direction_path": "theta(s)=(1,s/2),0<=s<=1",
    "minimum_path_norm": 1,
    "maximum_path_norm": "sqrt(5)/2",
    "source_locator": "manuscript9.4-9.5 and Section5",
    "kernel_threshold_claimed": false
  },
  "figure3": {
    "model": "mu=partial_x1 delta0 in R2",
    "exact_inverse": "E=-H(-x1) tensor delta0(x2)",
    "exact_support": "negative x1-axis",
    "direction": [
      1,
      0
    ],
    "A": 0,
    "p": 0,
    "N": 3,
    "n": 2,
    "supporting_halfspace": "x1<=0",
    "test_support": "closed disk center(2,0),radius1/2",
    "test_bump": "exp(-1/(1/4-|x-(2,0)|^2)) inside disk; zero outside",
    "exact_gap": "d=3/2",
    "combined_decay": "exp(-3 L h/2)",
    "upper_bound_function": "g_L=t^-3(log t)^6(1+L)^7exp(-3 L log(t)/2)",
    "normalization": "K=((7/c)^7 exp(-7+c))(6/e)^6,c=3log2/4",
    "retained_uniform_majorant": "g_L/K<=t^-2 for L>=0; t=2+|xi|^2",
    "plotted_safe_scales": [
      12,
      16,
      20
    ],
    "radial_samples": 701,
    "radial_interval": [
      0,
      6
    ],
    "integrand_measurements_claimed": false,
    "proof_locators": [
      "manuscript Section8 and Figure3",
      "learner Problems2,6,9"
    ]
  },
  "sample_checks_are_proofs": false,
  "reproducible_source": "make_figures.py",
  "generated_artifacts": [
    "logarithmic-cutoff-and-jacobian.png",
    "logarithmic-cutoff-and-jacobian.svg",
    "two-variable-graph-and-directions.png",
    "two-variable-graph-and-directions.svg",
    "support-plane-and-uniform-decay.png",
    "support-plane-and-uniform-decay.svg"
  ]
}