If I was initially lacking in the capital to do trades, I could publish my predictions online using public key cryptography and amass an impressive track record before recruiting investors.

This is a nitpick, but this protocol is at least underspecified. Aside from the need to prove that you made the predictions before the events, you also need to be able to prove that you made no other predictions before the event.

(I've always wondered why no pump-and-dump scammers use this: after ten "buy/short <volatile stock>" mails, 1/1024 of your mailing list will have received 10/10 correct predictions from you (and another 10/1024 will have received 9/10 correct predictions.) Which should be enough to convince quite a few to buy up some penny stock (with the scammer taking the other, profitable side of the trade.) In the spirit of this post, it's probably not profitable enough. Or spammers are stupid.)