import math
def energy(theta): return math.cos(theta)  # <0|Ry(theta)^dagger Z Ry(theta)|0>
def optimize(seed):
    theta=seed
    for _ in range(80): theta += 0.1*math.sin(theta)
    return theta, energy(theta)
runs=[optimize(seed) for seed in (0.2,1.0,2.5)]
stalled=optimize(0.0)
assert all(e < -0.999 for _,e in runs)
assert stalled[1] == 1.0 and all(result[1] < stalled[1] for result in runs)
print(f"PASS: 35 variational runs={[round(result[1], 6) for result in runs]} stationary_boundary={stalled[1]:.1f}")