The Probability Distribution of P-Values

On his facebook page, Nassim recently posted links to a new short technical paper on the probability distribution of p-values and a video commentary. He wrote:

I was able to pull out the exact meta-distribution of p-values (i.e. p-values as random variables).
The point is that the same phenomenon will produce p-values all over the map.  A true p-value of .12 will produce p-values <.05 more than half the time, so people may never replicate and get the same result.
One Hundred Years of P-Value Bullshit!

Here is the text of the paper, which was originally posted on his website, Fooled By Randomness.