{
  "lesson_id": "AN02-L143",
  "mean_transfer": {
    "real_dimension_of_picture": 2,
    "proof_locator": "HC3.1–HC3.2",
    "domain": "B(0,9/2)",
    "x": [
      0,
      0
    ],
    "r": "1",
    "a": [
      "3/16",
      "0"
    ],
    "s": "1/8",
    "y_j": [
      "1/4",
      "0"
    ],
    "exact_inclusions": [
      "B(a,s) subset B(x,r/2)",
      "y_j in B(a,s)",
      "B(x,r) subset B(y_j,2r) subset B(x,3r)",
      "closed B(x,4r) subset Omega"
    ],
    "integral_bound": "|C|*|B_r|+(|C|+D)*|B_2r|",
    "D": "B/|B(a,s)|+1",
    "meaning": "Exact illustrative geometry, not a sample function field"
  },
  "connected_cover": {
    "domain": "(-21/5,21/5) x (-6/5,6/5)",
    "compact_strip": "[-3,3] x [-1/10,1/10]",
    "centres_x_exact": [
      "-3",
      "-21/8",
      "-9/4",
      "-15/8",
      "-3/2",
      "-9/8",
      "-3/4",
      "-3/8",
      "0",
      "3/8",
      "3/4",
      "9/8",
      "3/2",
      "15/8",
      "9/4",
      "21/8",
      "3"
    ],
    "ball_radius": "1/4",
    "spacing": "3/8",
    "meaning": "Finite overlapping cover of a compact strip; not one uniform global bound"
  },
  "disconnected": {
    "domain": "B(-7/5,1) union B(7/5,1)",
    "values": [
      "0",
      "-j"
    ],
    "common_upper_bound": 0,
    "right_component_L1_norm": "pi*j",
    "proof_locator": "HC11 Example5"
  },
  "truncated_log": {
    "domain": "|z|<2",
    "sequence": "max(log|z|,-j)",
    "limit": "log|z|",
    "at_zero": [
      "-j",
      "-infinity"
    ],
    "support_of_difference": "|z|<exp(-j)",
    "unit_disc_error_exact": "(pi/2)*exp(-2*j)",
    "proof_locator": "HC10.1–HC10.3",
    "profile_j": [
      1,
      2,
      4,
      8
    ],
    "positive_radius_range": [
      0.0001,
      1
    ],
    "error_samples": [
      {
        "j": 1,
        "value": 0.21258416579381817
      },
      {
        "j": 2,
        "value": 0.028770138289325408
      },
      {
        "j": 3,
        "value": 0.0038936148141423704
      },
      {
        "j": 4,
        "value": 0.0005269434636862288
      },
      {
        "j": 5,
        "value": 7.13140429076575e-05
      },
      {
        "j": 6,
        "value": 9.65130619565578e-06
      },
      {
        "j": 7,
        "value": 1.3061622575923497e-06
      },
      {
        "j": 8,
        "value": 1.7676983908423413e-07
      }
    ],
    "compact_disc": "|z|<=exp(-2)",
    "disc_supremum": "max(-2,-j)",
    "singleton": [
      0,
      0
    ],
    "singleton_supremum": "-j",
    "disc_limit": -2,
    "singleton_limit": "-infinity"
  },
  "rendering": {
    "backend": "Agg",
    "TeX": false,
    "SVG_text": "editable",
    "PNG_dpi": 180,
    "figure1_pixels": [
      2880,
      1170
    ],
    "figure2_pixels": [
      2880,
      1062
    ]
  }
}