Hey hadarian,

Thanks for the questions.

You can checkout more information of the bridge here

But basically the bridge is a connection between Syscoin Assets and Ethereum ERC-20 tokens performed via a minting/burning process crosschecked by agents and validators, making it a trustless swap without any third-parties or P2P like atomic swaps. This enables ERC-20 tokens to come over to Syscoin and use it's protocol, and allows Syscoin Assets to move to ETH ERC-20 tokens to use it's protocol.

In a minting/burning fashion, the total supply will never increase/decrease, merely move between both chains.
For eg.
You have ERC20 token called CATS with 100k supply and you want to move over to Syscoin to use it's assets and Z-DAG(Zero Confirmation Transactions). You burn 50k(any amount) ERC20 + a fee, and move across to a Syscoin Asset called CATS. You will now have a 50k Supply on ERC-20 and a 50k supply on Syscoin side totalling the 100k. Then the same goes for moving back to ETH chain. You burn the 50k from SYS assets and move to the ETH ERC-20 side where CATS ERC20 is then minted again, bringing the ERC-20 supply back to 100k and Sys asset supply of CATS to 0.