For bitcoin hivemind:
Cashcoin IS bitcoin. Since there are 21 million bitcoin, if we moved all the bitcoin onto truthcoin, then there would be 21 million cashcoin.
If you have 1 bitcoin, you could move it from the bitcoin blockchain to the truthcoin blockchain, and it transforms into a cashcoin. So you no longer have any bitcoins, but you have 1 cashcoin. Then when you are done on truthcoin, you can move your cashcoins back to the bitcoin blockchain, and they become bitcoins again.
Truthcoin is going to be merge mined, similar to how namecoins works.
So it is being secured by the same hash power that secures the bitcoin blockchain.
A big limitation of merge mining is that if you have less than 1/2 the total mining hashpower supporting you, it is cheap to cause forks on your blockchain. Miners are paid to support you, but it wasn't enough for namecoin.
It isn't clear if namecoin is successful at merge mining. Their difficulty is 26 billion vs bitcoins difficulty of 179 billion, about 15% of the bitcoin miners are merge mined with truthcoin.
namecoin is securing domain names. Do you trust the bitcoin miners not to collude to hold your domain name for ransom?
truthcoin is securing the outcomes of predictions that people are betting large amounts of money on. Do you trust the bitcoin miners not to collude to hold the money in your prediction market for ransom?
Look at page 28 of the white paper near the bottom: http://bitcoinhivemind.com/papers/truthcoin-whitepaper.pdf
For Augur: ether are the cashcoin. https://blog.ethereum.org/2014/04/10/the-issuance-model-in-ethereum/
Currently it is secured by POW, but they are planning to move to POS.
For Flying Fox: flying foxes are the cashcoin. It has a new distribution method. https://github.com/BumblebeeBat/FlyingFox/blob/master/docs/coin_creation.mdhttps://github.com/BumblebeeBat/FlyingFox/blob/master/docs/coin_creation_price.md
Flying Fox is secured by a PoS consensus I invented that is based around the idea of payment channels.https://github.com/BumblebeeBat/FlyingFox/blob/master/docs/lightning_consensus.md