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    {
      "runId": "run-20260917003910210-62944-030",
      "label": "Logarithm · r=2 · -2 turns",
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      "runId": "run-20260917003910210-62944-031",
      "label": "Logarithm · r=2 · -3 turns",
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      "runId": "run-20260917003910210-62944-032",
      "label": "Logarithm · r=2 · -4 turns",
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          "label": "Input Re z",
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        {
          "label": "Input Im z",
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        {
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        {
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        {
          "label": "Continued Im w",
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        {
          "label": "Principal value Re w",
          "value": 0.6931471805599453,
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        {
          "label": "Principal value Im w",
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        {
          "label": "Maximum relation residual",
          "value": 2.094764613337708e-15,
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          "description": "Maximum |exp(w) − z| across both value conventions and every saved path sample."
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        {
          "label": "Path samples",
          "value": 513,
          "description": "128 angular intervals per complete turn, including the start and end."
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      ],
      "diagnostics": {
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      "plotSampleCounts": [
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          "title": "Continued output along the path",
          "series": "Re w",
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          "title": "Defining-relation residuals",
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          "title": "Defining-relation residuals",
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  "results": [
    "This saved batch contains 32 completed calculations. The table and downloads below refer to those actual runs.",
    "The largest recorded absolute diagnostic residual was 2.40178e-15. 32 of 32 residual-bearing cases were within their own reported numerical tolerance.",
    "Across 32 recorded readings, Unwrapped angle Θ ranged from -25.13274 to 25.13274.",
    "Across 32 recorded readings, Signed turns ranged from -4 to 4.",
    "Across 32 recorded readings, Output Re w ranged from -1.414214 to 1.414214.",
    "Across 32 recorded readings, Output Im w ranged from -25.13274 to 25.13274.",
    "On the saved unit-circle square-root runs, the continued endpoint after one positive turn was (-1, 1.22465e-16); after two it was (1, -2.44929e-16). Coordinates are (Re w, Im w); small nonzero imaginary parts reflect floating-point arithmetic.",
    "For the unit-circle logarithm, one positive turn gave Im w = 6.283185, and one negative turn gave Im w = -6.283185. The relation residual checks exponentiation at every saved path sample."
  ],
  "interpretation": [
    "Compare the signs or imaginary increments in the saved endpoint values while checking the defining relation along the path.",
    "A coincident input point does not imply the same continued output. Changing a branch cut would choose another single-valued representation without changing that relation."
  ],
  "summaryCsvPath": "/studies/complex/summary-20260917003910210-62944.csv"
}