{
  "schema": "AN02-L142-original-geometry141/v1",
  "Fourier_convention": "F(z)=integral exp(-i*s dot z) du(s)",
  "complex-triangle-envelope": {
    "proof_locators": [
      "MI4",
      "MI5",
      "MI7",
      "MI22–MI24"
    ],
    "support_points": [
      [
        -1,
        0
      ],
      [
        1,
        0
      ],
      [
        0,
        2
      ]
    ],
    "complex_coefficients": [
      {
        "real": 1,
        "imaginary": 0
      },
      {
        "real": 0,
        "imaginary": 1
      },
      {
        "real": -1,
        "imaginary": -1
      }
    ],
    "total_complex_mass": {
      "real": 0,
      "imaginary": 0
    },
    "total_variation": "2+sqrt(2)",
    "direction_eta": [
      1,
      1
    ],
    "support_line": "s1+s2=2",
    "support_value": 2,
    "real_alignment_frequency": [
      "pi/4",
      "-pi/2"
    ],
    "common_phase": "exp(i*pi/4)",
    "exact_envelope": "M(y)=log(exp(-y1)+exp(y1)+sqrt(2)*exp(2*y2))",
    "support_function": "h_K(y)=max(-y1,y1,2*y2)",
    "slice_y": "t*(1,1)",
    "sample_t_interval": [
      -3,
      3
    ],
    "sample_points": 1601,
    "proved_gap": "0<=M(y)-h_K(y)<=log(2+sqrt(2))",
    "metric": "Ordinary Euclidean metric, with equal coordinate scale in the support panel."
  },
  "signed-density-growth": {
    "proof_locators": [
      "MI2",
      "MI5",
      "MI7",
      "MI25–MI27"
    ],
    "density": "1_[-1,0](s)-1_[0,1](s) relative to ds; point values have no effect on the measure.",
    "support": [
      -1,
      1
    ],
    "total_mass": 0,
    "total_variation": 2,
    "endpoint_atomic_masses": [
      0,
      0
    ],
    "transform": "F(z)=2*(cos(z)-1)/(i*z), entire extension F(0)=0",
    "first_moment": -1,
    "transform_derivative_at_zero": "i",
    "exact_ray_modulus": "abs(F(i*t))=exp(t)*(1-exp(-t))^2/t for t>0",
    "exact_quotient": "1-log(t)/t+2*log(1-exp(-t))/t",
    "variation_upper_bound": "1+log(2)/t",
    "target_slope": 1,
    "sample_t_interval": [
      0.5,
      32
    ],
    "sample_points": 1400,
    "horizontal_axis": "Logarithmic t axis."
  },
  "rendering": {
    "PNG_dpi": 160,
    "SVG_text": "Editable labels using DejaVu Sans; the font notice accompanies the original sources."
  }
}