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  "plot_arithmetic": "NumPy float64; visualization only",
  "exact_presets": [
    {
      "A": [
        1,
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      ],
      "mean_square": "1",
      "rms": "1",
      "negative_depth": "9/8",
      "proof_identity": "cos(x)+cos(2*x)=2*(cos(x)+1/4)^2-9/8",
      "minimizer_formula": "acos(-1/4) and 2*pi-acos(-1/4)"
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      "mean_square": "1",
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  "phase_path": {
    "theta_1": "x modulo 2*pi",
    "theta_2": "2*x modulo 2*pi",
    "independent_all_negative_point": [
      "pi",
      "pi"
    ],
    "claim": "(pi,pi) is not on this path; it is allowed if phases are freed, changing the model"
  }
}