{
  "schema": "AN02-L151-exact-figure-geometry166/v1",
  "figure_A": {
    "nodes": [
      0,
      "epsilon"
    ],
    "multiplicities": [
      2,
      2
    ],
    "q": "-3*t^2/epsilon^2+2*t^3/epsilon^3",
    "normalized_q": "-3*epsilon*t^2+2*t^3",
    "displayed_epsilon": [
      0.2,
      0.4,
      0.8
    ],
    "unordered_D": "epsilon",
    "ordered_Delta": "epsilon^2",
    "usual_discriminant": "epsilon^2",
    "exact_supremum": "3/epsilon^2+2/epsilon^3",
    "supremum_attained_at_boundary_t": -1,
    "figure_curves_are_real_slices_of_the_exact_polynomial": true,
    "proof_locators": [
      "H1-H7",
      "H22-H24",
      "L151.1-L151.5"
    ]
  },
  "figure_B": {
    "graph": "(t,t^2) in C^2, real dimension 2 in real dimension 4",
    "panels_1_and_2_are_projections_not_the_full_graph": true,
    "unit_ball_b": "(sqrt(5)-1)/2",
    "parameter_radius": "sqrt(b)",
    "projection_radius": "b",
    "sample_t": "(9/20)*exp(i*pi/6)",
    "sample_opposite_t": "-(9/20)*exp(i*pi/6)",
    "projected_sample": "(81/400)*exp(i*pi/3)",
    "surface_density": "1+4*|t|^2",
    "projected_density": "4*|t|^2",
    "surface_minus_projected_density": 1,
    "fiber_count_nonzero": 2,
    "critical_projection_point": 0,
    "exact_surface_integral": "2*pi*(b^(3/2)/3+4*b^(5/2)/5)",
    "exact_fiber_integral": "8*pi*b^(5/2)/5",
    "proof_locators": [
      "H31-H32",
      "L151.11-L151.13"
    ]
  },
  "figures_are_original": true,
  "protected_book_media_used": false,
  "Blender_use": "The complex curve has four real ambient coordinates; exact plane projections and metric densities convey the map without an inexact 3D embedding."
}