Say I create my own currency in Open Transactions, and begin trading it on OT with other users. What prevents some user from creating copies of my currency? I'm not sure its the same situation as double spending. I'm talking about someone who doesn't have any of my money simply creating it out of thin air and selling it to other people.
In Open-Transactions, both parties have a copy of the "last signed receipt" for any given transaction.
The user forms the receipt and signs it, and then the server countersigns it.
Therefore the server cannot forge your receipt because the server does not have your private key.
When an issuer issues his currency onto an OT server, the server will have a copy of the issuer's "last signed receipt," which includes the server ID and shows the current amount that has been issued.
So the server cannot falsely claim to have a certain currency issued on that server, because the server cannot forge the issuer's signature (in the same way that the server cannot falsify your own receipt, since the server cannot forge your signature.)
The other users cannot forge your signature, nor can they forge the server's signature, nor can they forge the issuer's signature, so they cannot falsely issue units of your currency.
Also, each "last signed receipt" includes the current balance. For example, "My current balance is 100 clams. I am withdrawing 10 clams, and my new balance will thus be 90 clams." This receipt also contains the server ID, as well as the asset type ID, and must be signed by the user before being countersigned by the server. Therefore this is also true for the issuer's last signed receipt, the same as for any other user.
"The public key of the issuer must be INSIDE the contract. (In the sample contracts, it’s the first key that appears.)"
So a counterfeit issue would not have the right digital signature.
if i see it correctly, there is a certain statical data within each existing cryptocurrency client, that is used to interact with the entire network. for example, you can't create bitcoin from air and add it to an existing bitcoin network. it will have to match the tree of cryptographical operations so far. there is original bitcoin paper out there and https://en.bitcoin.it/wiki/Weaknesses to help you better understand the possible problems and issues of bitcoin network.