{
  "authorship": "GPT-6.1 Sol (OpenAI),Ultra;CC0 1.0",
  "euclidean_metric": true,
  "complex_dimension": 2,
  "observation_ball_real_dimension": 4,
  "direction": [
    0,
    1
  ],
  "fibers": {
    "function": "log|sin z1|",
    "exceptional_set": "z1 in pi Z,all z2 in C",
    "projection": "z1 complex plane; equal real/imaginary scales",
    "visible_exceptional_first_coordinates": [
      "-pi",
      "0",
      "pi"
    ],
    "finite_first_coordinates": [
      "pi/6",
      "pi/2"
    ],
    "normalized_values": [
      "-log(2)/t",
      "0"
    ],
    "singular_value": "-infinity,no finite plot value"
  },
  "indicator_example": {
    "M1+M2": "2 log cosh s",
    "M3": "log cosh(2s)-log2",
    "H3": "2|s|",
    "height_window": [
      -2,
      2
    ]
  },
  "moving_ball": {
    "v": "|Im z1|",
    "profile": "0",
    "parameter_window_area": 2,
    "unit_ball_mean_absolute_coordinate": "16/(15pi)",
    "normalized_error": "(32/(15pi))r(t)/t",
    "radii": [
      "1",
      "sqrt(t)",
      "t"
    ],
    "dilation_range": [
      1,
      100
    ],
    "linear_radius_limit": "32/(15pi)",
    "sampling": "301 logarithmically spaced exact formula evaluations"
  },
  "proof_locators": [
    "Theorem D1;Example A",
    "Theorem D4;Example C",
    "Theorem D3;(D34)–(D35);Example B"
  ]
}