To be honest, I am a little reluctant to publish it here, as I intend to do so later “officially” under my real name, and I’d like to maintain at least a semblance of separation between my presence here and my real identity.
I published an earlier, more undeveloped proof and exposition of the Law of Returns along Austrian lines using Mathematics for illustration in the following older thread. Unfortunately the links to my uploads are broken since they expired. Here’s the “latest” version in pdf format, which is the same as the file I last uploaded quite a few months ago in that thread, so it’s quite far from the final formulation I currently only have in written format. I might present it as part of a larger paper on price theory at an upcoming conference, if I can get all the damn reading and writing done in time!
If you wish, you could add me as a friend and send me a PM with your email. I’ll send you the complete version when I’ve finished typing it up.
@ I.Ryan, I’ll have to get back to you on that; it’s in one of my old notebooks that I don’t currently have with me.