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  ],
  "coordinate_formulas": [
    "cos(x)",
    "cos(2*x)",
    "cos(3*x)"
  ],
  "exact_constraints": [
    "y = 2*u^2 - 1",
    "z = 4*u^3 - 3*u",
    "u = cos(x)"
  ],
  "colour": "sum of coordinates; linear viridis scale -1.4 to 3",
  "parameterization": "x in [0,2*pi]; second half retraces the first",
  "scope": "Amplitude-coordinate illustration, not physical-space motion, independent phase filling, or probability density",
  "plot_arithmetic": "float64; the two polynomial constraints are exact identities"
}