Ultra Terminum

Proof of Reflection starts with two chains: each records and checks the other’s block headers and counts the other’s work when it picks between competing histories. Ultra Terminum does this across many chains at once: every simplex chain reflects every other. Simplex explains why that protects each chain.block header - A block’s summary: it commits to every transaction in the block and links to the block before it.

Ultra Terminum doesn’t run a chain by itself. It changes how each chain picks its history, its fork rule, so that many chains can cooperate.fork rule - How a chain picks between competing histories, by comparing the work behind each.

To compare histories, a chain adds up the weight of each: its own work plus the work of other chains’ blocks that record it, after conversion into its own units.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.conversion - How a chain counts another chain’s work in its own units, so that its fork rule can compare the two.

Ultra Terminum is proof-agnostic: it is designed to work with Proof of Work, Proof of Stake and other kinds of consensus. Amaroo’s simplex chains use Proof of Work, in which miners spend computing power to build blocks. It suits reflection:Proof of Stake - Consensus in which validators stake tokens they can lose if they cheat.Proof of Work - Consensus in which block producers spend computing power to build blocks.miner - A node that builds blocks on Amaroo’s simplex chains and adds its hash power to the network.

• A measurable, unforgeable cost. Work takes real resources, so it can be counted and converted between chains.
• Readable from the block. A block’s header shows the work that went into it, and checking it is quick.
• No validator set to track. Checking work takes only headers, not a list of who may sign blocks, which suits light clients.light client - Software that uses a network by checking block headers and proofs instead of downloading every block, light enough for a phone.
• Plug and play. Mining needs hardware and power, and little else.

The network is designed so that chains with different Proof of Work algorithms, one assigned to each simplex chain, collaborate and secure one another through conversion of work. Dapp-chains run whatever consensus their builders choose.

On a single chain, a transaction gains one confirmation per block. In the simplex, each new block also records the other chains’ latest blocks, adding weight to their histories too. Blocks land on different chains at different moments, so confirmations arrive in waves, far more often than any one chain makes blocks. The design counts confirmations from other chains like a chain’s own; the whitepaper tests this in simulation and works through the theoretical confirmation rate.wave - The rhythm of confirmations across the network: the chains’ blocks are offset in time, and each chain counts the others’ work, so confirmations are designed to arrive far more often than any one chain’s blocks.

Ultra Terminum grows in configurations, each built on the last: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.

• UT1, the simplex. Simplex chains that all reflect one another.
• UT2, dapp-chains. Application chains that can be anchored to the network.
• UT3, nested dapp-chains. Dapp-chains that host chains of their own, a further step the whitepaper sketches.
• Tiling. Simplexes joined to one another. A research direction, not a feature.

Each configuration adds capacity to the one before. The whitepaper works through the theoretical capacity of each configuration.

Amaroo is designed for decentralization through heterogeneity: people take part with the computing power they have.

• Miners build blocks on the simplex chains, adding the work the network counts.
• Non-mining nodes help gossip messages across the network.non-mining node - A node that helps gossip messages across the network without building blocks.
• Light clients use the network from phones and other light devices.