📈Bonding Curve

Since v2.4.0, Flap supports multiple bonding curves, but only one is active.

What is a Bonding Curve

Before listing on DEX, each token launched on flap is bonded to a bonding curve. When you buy tokens from the bonding curve, you send your ETH (or other quote token, usually the native token of that chain) to the bonding curve as a reserve, and the bonding curve mints tokens to your address. Or if you sell your tokens to the bonding curve, the bonding curve would burn your selling tokens and send the ETH back to you.

A bonding curve defines the relationship between the trading token's supply and the reserve (i.e. Quote tokens like ETH or BNB). The change of the reserve respect to the supply is the price. Our bonding curve is based on a constant product equation. You may have heard about this equation, which Uniswap popularized.

You may even wonder what is the difference between a bonding curve token launching platform like flap and Unsiwap? The answer is the liquidity. The liquidity does not change on the bonding curve. However, anyone can add liquidity to the Uniswap pools.

Flap's Bonding Curve V2

The token created on our platform has the same max supply of $10^9$ , with 18 decimals. For each token, the amount of token and the ETH (the native token of the target chain) follow the following constant product equation:

$$(x+ h)(y + r) = K$$

$r$ ,$h$ and $K$ are constant parameters dependent on the target chain ( check Bonding Curves On Different Chains for more details).

$$(x+ h)(y + r) = K$$

• $x$ is the amount of token in the bonding curve, initially, it is $10^9$, which means all the tokens are still in the bonding curve.

• $y$ is the amount of ETH , it is 0 in the beginning.

• Our curve have 3 constant parameters:

  • $r$ can be interpreted as the virtual reserve of ETH in the bonding curve

  • $h$ can be interpreted as the virtual reserve of token in the bonding curve

  • $K$ is the square of the virtual liquidity

To better understand the bonding curve, we use $s$ to denote the token's current (circulating) supply. And the relationship between $s$ and $x$ is straightforward:

$$x = 10^9 - s$$

We can get the following relationship between $s$ and $y$ :

$$(10^9 + h - s)(y + r) = r \cdot 10^{9}$$

Based on the above equation, we can get the relationship between the circulating supply and ETH in the bonding curve.

Bonding Curves On Different Chains

For different deployment and different payment token, the constants are different:

Chain	r	h	K
BSC (Legacy before block #42042177 )	15	0	$15 \cdot 10^{9}$
BSC (Legacy since block 42042177 and before 47855189 )	4	0	$4 \cdot 10^{9}$
BSC (Legacy since block 47855189 and before 51314696)	2	0	$2 \cdot 10^{9}$
BSC(latest, BNB as payment Token)	4	0	$4 \cdot 10^{9}$
BSC(latest, USD1/lisUSD as payment token)	2500	0	$2500 \cdot 10^{9}$
ToshiMart	0.5	0	$0.5 \cdot 10^{9}$
XLayer (Before block 31564005)	28	0	$28 \cdot 10^{9}$
XLayer (Before block 32470187)	21.25	0	$21.25 \cdot 10^{9}$
XLayer(Since block 32470187)	28.25	108002126	31301060059