{
  "factorization": "x**2*(x - 1)**3*(4*c*(x**4 + x**3 + x**2 + x + 1)*(3*x**5 + 6*x**4 + 9*x**3 + 12*x**2 + 8*x + 4) + (x - 1)*(3*x**8 + 12*x**7 + 30*x**6 + 60*x**5 + 98*x**4 + 137*x**3 + 170*x**2 + 159*x + 66))/210",
  "positive_derivative_numerator": [
    735,
    4410,
    11655,
    20580,
    28560,
    31290,
    26740,
    17850,
    9030,
    3080,
    420
  ],
  "unique_boundary_x": [
    "2003/2500",
    "80121/100000"
  ],
  "interpretation": "cp decreases with x and increases with h=-log(x). For LONGER pulses beyond the crossing AB wins for all feasible c; for shorter pulses both preferences exist.",
  "source_note": "The manuscript Figure 2 caption reverses its below/above-h0 description. This example follows Proposition 3 and the directly checked monotonicity."
}