{
  "authorship": "Original mathematics and figures; GPT-6.1 Sol (OpenAI), Ultra; CC0 1.0",
  "neighborhoods": {
    "centers": "c_j=2^j",
    "indices": [
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    "parameter_radii": [
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    "frequency_radii": [
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    "relative_radii": [
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    "point_mass": -1,
    "profile": "-Im(z)",
    "carrier": [
      -1
    ],
    "proof_locators": [
      "Learner Example 1",
      "Formal Lemma 1.1",
      "Formal Theorem 3.1"
    ]
  },
  "translations": {
    "model": "log|sin(z+a)|",
    "translations": [
      0.0,
      1.5707963267948966
    ],
    "zero_formula": "z=m*pi-a, m integer",
    "shown_zero_sets": [
      [
        -6.283185307179586,
        -3.141592653589793,
        0.0,
        3.141592653589793,
        6.283185307179586
      ],
      [
        -4.71238898038469,
        -1.5707963267948966,
        1.5707963267948966,
        4.71238898038469
      ]
    ],
    "envelope": "log(cosh(eta))",
    "indicator": "abs(eta)",
    "carrier": [
      -1,
      1
    ],
    "display_clip": [
      -3,
      2
    ],
    "zeros_have_value": "-infinity",
    "compact_Fourier_realization_asserted": false,
    "proof_locators": [
      "Learner Example 4",
      "Formal Lemma 2.1",
      "Formal Corollary 2.3"
    ]
  },
  "references": [
    "Terence Tao, 246B Notes 2",
    "Lars H\u00f6rmander, Analysis of Linear Partial Differential Operators I and II"
  ],
  "Blender_applicability": "Flat frequency-radius graphs and exact complex-parameter heatmaps need no three-dimensional scene."
}