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You’re right, the 2^(-3/4) (and the 2^1/4) is probably quantitatively wrong (unless each side is perfectly heat-conducing but both are isolated from each other. Or if the planet is a coin facing the sun. You know, spherical cows in a vacuum…). But I don’t think that changes the qualitative conclusion, which hold as long as the bright side is hotter but not twice as hotter than the perfectly-heat-conducing planet.
Oh, yes, it does change, of course.
The result, that a faster rotating planet is warmer, is against the Al Gore's theology about Climate Change, formerly known as the Global Warming.
As Scott Alexander said - the scientific community consensus was wrong, I was right.
I am not sure about him, I know I am right here and the "science community" as it is self-proclaimed - is wrong.
A faster rotating planet is warmer.