Simplex
The simplex is the network Amaroo’s chains form when every chain reflects every other: in the whitepaper’s words, “many blockchains becoming one coherent network.”
Each records and checks the others’ and counts their work when it picks its history. The simplex is Ultra Terminum’s first , UT1.simplex chain - One of Amaroo’s own chains. Each reflects every other chain in the simplex.block header - A block’s summary: it commits to every transaction in the block and links to the block before it.configuration - One of Ultra Terminum’s ways to arrange chains: the simplex alone, the simplex with dapp-chains, deeper nesting, and tiling, a research direction.
Fig. 1
Two chains share 1 mutual reflection, seven share 21 and seventeen share 136 (whitepaper, Figure 12).
The name comes from geometry. Draw each chain as a point and each mutual reflection as a line, and the drawing is a simplex: a line for two chains, a triangle for three, a tetrahedron for four.
One chain, as hard as the network
The simplex is designed so that attacking one chain is as hard as attacking the whole network: a chain’s counts the work of every block on other chains that records it, so an attacker would need more work than all of the network’s honest together (whitepaper, section 4.10.1).weight - What a fork rule compares: the work behind a chain’s blocks, summed. Under Proof of Reflection it also counts the converted work of the blocks that reflect the chain.miner - A node that builds blocks on Amaroo’s simplex chains and adds its hash power to the network.
The chains don’t have to be identical. In Amaroo’s design each runs the mining algorithm assigned to it and images its own set of ; to is to record and check another chain’s headers.foreign chain - A chain outside Amaroo’s network, such as Bitcoin or Ethereum. Amaroo images foreign chains one way; it doesn’t reflect them.image - To record and check another chain’s block headers. The whitepaper calls the record a projection.
Where the books live
The simplex also carries the exchange. Each coin’s lives on the simplex chain that images that coin’s chain, priced against . The book is chain state, so orders are matched as that chain builds blocks. DEX infrastructure follows a trade end to end.connected - Joined to Amaroo by imaging. A connected chain is a foreign chain that Amaroo’s chains image, and a connected coin is that chain’s coin; Amaroo’s own chains are simplex chains.book - An order book: the orders resting to buy and sell one coin against ROO. Each connected coin’s book is chain state on the simplex chain that images that coin’s chain.ROO - The network’s token. It pays fees, every order book is priced against it, and it is locked as collateral and escrow while trades settle.
How big a simplex gets
Every chain records every other chain’s headers, so each new chain takes up a little room in all the others’ blocks, and a simplex has a best size. To grow past it, the whitepaper sketches : joining simplexes to one another. It is a research direction, not a feature. Ultra Terminum sets out the network’s configurations.tiling - A research direction: joining simplexes into a larger network, with neighboring simplexes reflecting each other.
Terms
- simplex chain
- One of Amaroo’s own chains. Each reflects every other chain in the simplex.
- block header
- A block’s summary: it commits to every transaction in the block and links to the block before it.
- configuration
- One of Ultra Terminum’s ways to arrange chains: the simplex alone, the simplex with dapp-chains, deeper nesting, and tiling, a research direction.
- mutual reflection
- When two chains each record the other’s headers and count the other’s work.
- weight
- What a fork rule compares: the work behind a chain’s blocks, summed. Under Proof of Reflection it also counts the converted work of the blocks that reflect the chain.
- miner
- A node that builds blocks on Amaroo’s simplex chains and adds its hash power to the network.
- foreign chain
- A chain outside Amaroo’s network, such as Bitcoin or Ethereum. Amaroo images foreign chains one way; it doesn’t reflect them.
- image
- To record and check another chain’s block headers. The whitepaper calls the record a projection.
- connected
- Joined to Amaroo by imaging. A connected chain is a foreign chain that Amaroo’s chains image, and a connected coin is that chain’s coin; Amaroo’s own chains are simplex chains.
- book
- An order book: the orders resting to buy and sell one coin against ROO. Each connected coin’s book is chain state on the simplex chain that images that coin’s chain.
- ROO
- The network’s token. It pays fees, every order book is priced against it, and it is locked as collateral and escrow while trades settle.
- tiling
- A research direction: joining simplexes into a larger network, with neighboring simplexes reflecting each other.
Definition
Simplex
The single coherent structure that emerges from a collection of blockchains that mutually reflect each other.
Whitepaper v1.1, section 3.2, p. 38. The simplex is designed so that attacking one chain is as hard as attacking the whole network (section 4.10.1, p. 78).