{
  "schema": "LC035-exact-figure-geometry/v1",
  "crossing": {
    "polynomial": "(tau-eta1)(tau-eta2)",
    "normal": [
      1,
      0,
      0
    ],
    "crossing_frequency": [
      1,
      1,
      1
    ],
    "simple_frequency": "(1,1,1+d), d != 0",
    "noncharacteristic_frequency": "(1,1+d,1+d), d != 0",
    "component_slice": "v_tau=1",
    "crossing_component_inequalities": [
      "v1<1",
      "v2<1"
    ],
    "simple_component_inequalities": [
      "v1<1"
    ],
    "polar_slice": "x_tau=1",
    "crossing_polar_segment": [
      [
        -1,
        0
      ],
      [
        0,
        -1
      ]
    ],
    "simple_polar_point": [
      -1,
      0
    ],
    "noncharacteristic_polar_slice_empty": true
  },
  "wave": {
    "polynomial": "tau^2-eta1^2-eta2^2",
    "normal": [
      1,
      0,
      0
    ],
    "field": "(0,-tau*eta/(tau^2+|eta|^2))",
    "angles_radians": [
      0,
      1.0471975511965976,
      2.0943951023931953
    ],
    "frequency_trajectory": "xi_star=(1,1,0)/sqrt(2)",
    "F_trajectory": "eps^2/4 +/- i*eps/sqrt(2)",
    "meridian": "xi=(tau,sqrt(1-tau^2),0), -1<=tau<=1",
    "eps_meridian": 0.25,
    "proved_uniform_lower_bound": 0.0625,
    "all_boundaries_and_directions": "exact formulas; sampled only for rendering"
  },
  "proof_locators": [
    "LC035-2",
    "LC035-3",
    "LC035-4",
    "lesson E1-E3"
  ],
  "not_claimed": [
    "full cone volumes drawn",
    "sampling establishes theorem",
    "root multiplicity is a simple-root count"
  ]
}