{
  "fourier_convention": "F(z)=mu(exp(-i*x.z))",
  "finite_difference": {
    "kernel": {
      "points": [
        -0.5,
        0.5
      ],
      "coefficients": [
        1,
        2
      ]
    },
    "zeros": "z_j=(2*j+1)*pi-i*log(2), j integral",
    "displayed_indices": [
      -3,
      -2,
      -1,
      0,
      1,
      2,
      3
    ],
    "displayed_real_center_window": "abs(eta)<=log(2+abs(xi))/3",
    "window_is_a_real_center_comparison_not_the_total_complex_norm_strip": true
  },
  "ratio_panel": {
    "indices": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20,
      21,
      22,
      23,
      24,
      25,
      26,
      27,
      28,
      29,
      30,
      31,
      32,
      33,
      34,
      35,
      36,
      37,
      38,
      39,
      40,
      41,
      42,
      43,
      44,
      45,
      46,
      47,
      48,
      49,
      50
    ],
    "difference_ratio": "log(2)/log(sqrt(((2*q+1)*pi)^2+log(2)^2))",
    "elliptic_branch": "z=(t,i*sqrt(1+t^2)), t=q+1",
    "elliptic_symbol": "1+z1^2+z2^2",
    "elliptic_ratio": "sqrt(1+t^2)/log(sqrt(1+2*t^2))",
    "one_branch_not_an_all_zero_proof": true
  },
  "boundary_profiles": {
    "positive_center": "v(z)=Im(z)",
    "negative_center": "v(z)=-Im(z)",
    "parametrix_profiles": "the negatives on the same centers",
    "kernel_and_parametrix_singular_sets": [
      -1,
      1
    ],
    "convex_hull": [
      -1,
      1
    ],
    "interior_is_smooth": true
  },
  "translated_example": {
    "a": 0.6,
    "kernel_singular_set": [
      0.6
    ],
    "inverse_singular_set": [
      -0.6
    ]
  },
  "proof_locators": [
    "Formal Theorem2.1,Theorems3.4,4.1,5.1",
    "Learner Examples1,2,4 and Exercise3"
  ],
  "source_credit": "Original diagrams of the explicitly proved models; H\u00f6rmander convolution regularity theory is credited in both chapters."
}