from math import sqrt
def extrapolate(e1, e3, sigma1, sigma3):
    return (3 * e1 - e3) / 2, sqrt((1.5 * sigma1) ** 2 + (0.5 * sigma3) ** 2)
def majority(bits):
    return int(sum(bits) >= 2)
baseline = extrapolate(.74, .62, .02, .03)
counterfactual = extrapolate(.74, .68, .02, .03)
single_flips = [majority(tuple(int(i == j) for i in range(3))) for j in range(3)]
double_flip = majority((1, 1, 0))
assert abs(baseline[0] - .8) < 1e-12 and baseline[1] > .03
assert counterfactual[0] < baseline[0] and single_flips == [0, 0, 0] and double_flip == 1
print(f"PASS: 46 mitigation={baseline[0]:.3f}+/-{baseline[1]:.3f} shifted={counterfactual[0]:.3f} corrected={single_flips}")