Deflationary xToken

Why moon?

xToken is driven by the burn mechanics of xNFT as described above. As supply of xTokens decrease, the price of xToken is designed to increase.

$$P=\frac{M}{S}$$

Price is determined by Market Cap divided by the total supply of xToken. Thus,

$$P=\text{price}\\ M=\text{market cap}\\ S=\text{total supply}$$

Given that the new supply changes according to the burn mechanism of mint and trade, the denominator of the price equation can be represented as the new supply.

$$S_{1} = S_{0}-Burn_{m}-Burn_{t} \\ S_{1} = \text {new supply} \\ S_{0} = \text {old supply} \\ Burn_{m} = \text{supply burnt from mint} \\ Burn_{t} = \text{supply burnt from trade}$$

Burnt supply from both mint and trade can be summarized by summation of all instances of mint or burn, determined by the price in xToken and burn fee at the period of action. To give burn supply of mint as an example,

$$\sum_{i=1}^n P_{mi} B_{mi}\\ n = \text{number of mints}\\ P_{mi}=\text{price of mint at instance i}\\ B_{mi}=\text{burn fee in percentage of mint at instance i}$$

To combine everything, we get the price appreciation equation where price is determined by the burnt supply from mint and the fees that occur from trades, as follows.

$$P_{1} = \frac{P_{0}S}{S - \sum_{i=1}^n P_{mi} B_{mi} - \sum_{j=1}^m P_{tj} B_{tj}}\\$$

$$P_{1}=\text{new xToken price}\\ P_{0}=\text{old xToken price}\\ S=\text{xToken supply}\\ n=\text{number of mints}\\ P_{mi}=\text{price of mint at i}\\ B_{mi}=\text{mint burn fee in percentage at i}\\ m=\text{number of trades}\\ P_{tj}=\text{price of trade at j}\\ B_{tj}=\text{trade burn fee in percentage at j}$$