Radix is built on a combined architecture and consensus algorithm called Tempo, which is fully outlined in the Tempo white paper that can be found here: http://bit.ly/2ADK8LA
The aim of Tempo is to create a trustless, decentralized consensus algorithm that can work reliably as a public network. To do this it must be:
To achieve this, Tempo relies on a two simple ideas, and one logical leap:
A logical clock is a counter that is incremented by 1 every time something new happens. On Radix, “something new” is when one Node speaks to another in the Radix network. This gives every Node their own relative time, based on network activity, and one they can use to create a simple order of events.
Gossip protocols are well established in computer science and are one of the fastest ways in which information can be reliably shared across a network. It works simply by a Node choosing a couple of other Nodes to tell something new to, and they, in turn, tell two other Nodes, and so on and so on. This causes information to spread at an exponential rate.
On Tempo, we add the Node logical clocks, signed by the Nodes in question, to the gossip they are spreading around the network. This allows everyone to see both new information, and at what logical clock time that information was seen by other members of the network.
To allow high scalability a Tempo ledger is split into a very large shard space, allowing a huge degree of concurrency. To avoid a double spend across any of the shards, the shard a wallet lives on is determined by its public key. This makes sure that any spend from a wallet will always start on the same shard.
When combined with the logical clocks and gossip, this Tempo to always find the total ordering of related events, allowing double spends to be quickly detected and ignored.