# Concept Math Spec

:::warning
Do we want to multiple levels of state i.e global vs local?
:::

## State Variables

| Name | Description | Symbol |
|----|----|----|
| ETH Price | Price of Ethereum token in the current state | $P$ |
| Time | Index of current state | $t$ |
| Epoch | Index of the current epoch | $e$ |
| Validators | Current number of validators | $V$ |
| Validator index | Index of a unique validator | $i$ as in $V_i$|
| Commitees | Current number of commitees in a given epoch | $C$ |
| Staking Reward | Rewards received by a validator for staking, denominated in ETH | $R$ |
| Block Proposer Reward | Rewards received for proposing a block, denominated in ETH | $B$ |
| Penalty | Penalties incurred by validators, denominated in ETH | $\pi$ |
| Slash | Slash events experienced by validators |$\psi$|
| Total ETH Staked | | $S$ |
| Validator Yield | | $Y$ |

## Stateful Parameters
Stateful parameters are used to maintain a global state or aggregate state, if it exists. The distinction between stateful parameters and the state variables in the higher level state is nuanced.

:::warning
It may be the case that we don't need a seperate stateful parameter set, so this is a placeholder
:::

## Stateful Metrics
Stateful metrics are employed to measure the performance of the system