I didn’t see you had to sign the remainder, my bad.

Next question: Let’s say I have 100 tokens. I use the first spend to buy sth that is worth the equivalent of 49 Tokens (i.e. some BTC) and set the remainder to be a “stake” of 51 Tokens. The merchant will accept it because my stake is ≥ 50%. Then I buy another 25 Tokens of BTC and set the remaining stake to be 26 Tokens and so on.

The more often I repeat this, the lower my actual “stake” will be. The stake will be 0,5^x where x is the amount of times I repeat this.

Let’s say after 10 spend I will double spend the first one. Then I will loose 0,1 tokens and all the other people will loose 99.9 tokens. How is that secure?