# Liveness Properties

In MOI network, Modulated Trust is a feature that consists of MOI consensus protocol and context-driven ICS mechanism, where, based on the interaction type and context type, leader election is done within the same set of contexts driven or wallet driven nodes, ensures that there will be no other ICS for the same interaction, resulting in single and stand-alone tesseract for that particular interaction and eliminating the concepts of forking/forks and managing the account state without interruptions.

## Proof of Liveness​

In order to ensure the liveness of the MOI network, we make sure that the context associated with the wallet will not be absolute. Meaning, there probably won’t be a scenario where all nodes belonging to a wallet context will be down/unavailable at the same time.

As mentioned in the participant context section, for every wallet we capture the context in 3 dimensions i.e., alpha, beta, and gamma.

And the context size will always have a relation with the network size i.e.,

$n(\alpha U β U Ɣ) >= max(LW,LU)$

Meaning, that a minimum of 5 nodes make up a wallet’s context but grows up to 5% of the total number of nodes that exist in the network.

Every time an ICS is formed, the beta nodes are replaced with a new set of random nodes that participated in the ICS, thereby increasing the randomness and eventually decreasing the risk of context becoming absolute.

Also, in most cases, gamma remains constant and there is a correlation between alpha and beta nodes in a wallet’s context:

$n(β) = max(LW, LU) – n(Ɣ ) - n(\alpha ),$

where M is a constant percentage value set in the protocol, for example, 5% of the total size of the network. Over time when the network growth reaches a steady-state, the beta nodes will be replaced by alpha nodes.

Also, to ensure that no deadlock happens while choosing a leader out of the context nodes of a sender, everyone has a fair opportunity to maintain the network, using the Proof of Staking mechanism. We use a weighted round robin-based leader election mechanism to elect Generators for each ICS cluster.

Apart from understanding the general safety and liveness properties, let us take a look at how the MOI network addresses the common attack vectors.