{
  "schema": "AN02-radial-geometry252/v1",
  "exact_sphere_geometry": {
    "dimension": 2,
    "center": [
      "1",
      "-1/2"
    ],
    "radius": "3/2",
    "unit_direction": [
      "3/5",
      "4/5"
    ],
    "singular_point": [
      "19/10",
      "7/10"
    ],
    "reflected_center": [
      "-1",
      "1/2"
    ],
    "reflected_point": [
      "-19/10",
      "-7/10"
    ],
    "singular_sets_are_circles_not_filled_disks": true,
    "higher_dimension_picture_is_section": true,
    "proof": "Proposition 10.1; exact reflection in equation (10.2)"
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  "proved_bounds": {
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    "dimension3": "W_3-1=0",
    "dimension5": "W_5-1=-i/r"
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