a. Data Collection

Assume a project has expanded its tokenomics in a n-number of multichain environment, we define $CS_{C_{all}}(t)$, a $CirculatingSupply$ covering set of all chains $C_{all} = \{C_1, C_2, C_3, ..., C_i, ...C_n \}$, at a specific time $t$.

Then we can define $CirculatingSupply_{C_{all}}$ including all chains the project has launched its token contract, $CS_{C_{all}}(t)$ accumulated in parallel (added orderly from $C_1$ to $C_n$) as follows:

$$CS_{C_{all}}(t) = CS_{C_1}(t)+ CS_{C_2}(t)+...CS_{C_i}(t)+ CS_{C_{n-1}}(t) + CS_{C_n}(t) = \sum_{i=1}^{n}CS_{C_{i}}(t)$$

Likewise, other supply related concepts such as $TotalIssued_{C_{all}}$, $TotalBurnt_{C_{all}}$, $TotalSupply_{C_{all}}$, and $NonCirculatingSupply_{C_{all}}$ can all be defined in multichain environment with respect to specific time $t$, each illustrated by sum of $TI_{C_i}(t)$, $TS_{C_i}(t)$, $TB_{i}(t)$, and $NCS_{i}(t)$ for each $C_{i}$ in set of all chains $C_{all}$ as follows:

$$TotalIssued_{C_{all}}=TI_{C_{all}}(t) = \sum_{i=1}^{n}TI_{C_i}(t)$$

$$TotalBurned_{C_{all}} = TB_{C_{all}}(t) = \sum_{i=1}^{n}TB_{C_i}(t)$$

$$TotalSupply_{C_{all}} = TS_{C_{all}}(t) = \sum_{i=1}^{n}TS_{C_i}(t)$$

$$NonCirculatingSupply_{C_{all}} = NCS_{C_{all}}(t)= \sum_{i=1}^{n}NCS_{C_i}(t)$$

And $CirculatingSupply$, for chain $C_i$:, $CirculatingSupply_{C_{i}}$: $CS_{C_i}(t)$ and their relationship between consisting values: $TI_{C_{i}}$, $TS_{C_i}(t)$, $TB_{i}(t)$, and $NCS_{i}(t)$ can also be defined by implementing a single-chain logic for each chain illustrated as follows:

$$CS_{C_i}(t) = TI_{C_i}(t) - TB_{C_i}(t) - NC_{C_i}(t)$$