Mechanism Paper

80% of tokens are placed on the bonding curve, and the price is determined by the following exponential bonding curve:

$$P(x) = P_0 \cdot e^{k \cdot x}$$

Where:

• $P(x)$ is the price of the token at a given point $x$

• $P_0$ is the initial price of the token

• $k$ is the constant which is used to define the token's intended price range along the bonding curve

• $x$ is the percentage of tokens sold (ranging from $0$ to $1$)

We established the following price range based on three key criteria:

1. Should provide sufficient purchase opportunities to many small retail participants

2. Locked liquidity should exceed $10k

3. Memeable price points (69420!)

The simulation resulted in these optimal parameters:

$$P_{\text{Token}_\text{initial}} =0.0000042 \text{ S}$$

$$P_{\text{Token}_\text{final}} =0.000069 \text{ S}$$

$$k = \ln(\frac{P_{\text{Token}_\text{final}}}{P_{\text{Token}_\text{initial}}}) = \ln(\frac{0.000069}{0.0000042}) \approx 2.7990219793079367$$

The total liquidity gathered after the bonding curve sale will amount to $18,800 S$, excluding additional trading fees (currently at 1%).

Given that $P_{\text{Token}_\text{final}}$ is $0.000069 S$ and $200,000,000$ tokens are deployed to the CPAMM, $13,800 S$ of liquidity should be added to the V2 pool to establish consistent pricing between the bonding curve's final price and the CPAMM supply price. The remaining S after the liquidity provision will be retained by the protocol.