It will be easiest for me to explain Jute by starting with Bitcoin-style consensus and modifying it. And the first change to make is to allow blocks to have multiple parents. This changes our 'chain' into a directed acyclic graph, or 'rope' (also called a braid or a tangle). A block can have multiple parents, but no parent can be an ancestor of another parent. Banning ancestor inclusion is not strictly necessary, but makes implementation easier. Turning the blockchain into a rope means that multiple blocks can be mined in parallel, and then later merged into the chain. In Bitcoin style consensus, when two blocks are mined with the same parent, one will definitely become an orphan. By allowing a child block to point to multiple parents, we can enable both blocks to be included in the chain, meaning that both may be able to get block rewards.
Unmerged chaintips are called 'threads', and may consist of multiple bl