The Bonding Curve

How to make it go brrr?

Bonding curves establish a clear relationship between token supply and price. As more tokens are minted (or burned), the price per token adjusts according to a predefined mathematical function.

The bonding curve increments the token price in clear, predefined steps as more tokens are bought or sold. This provides clarity and predictability for the user.

Printr’s chain-agnostic bonding curve mechanism establishes a clear relationship between supply and price, independent of the specific blockchain.

We're currently using Meteora’s bonding curve (single-chain) for Solana for token availability across DEXs and trading tools. Once EVM is available, we'll use our custom chain-agnostic bonding curve across chains with full support for token migration

If a token graduates, you can participate in the bonding curve of any asset on any chain with cross-chain swaps enabled.

The expression for the curve is:

$$f(x) = \frac{MP(x + a)}{M - (x + a)}$$

where:

• M = Maximum token supply

• P = Base price factor

• x = New supply added

• a = Virtual reserve (used to smooth pricing)

You can learn more about the bonding curve from the Curve Math page.

The implications of using this bonding curve expression are:

• Once the specified token supply is sold, the contract graduates the token and moves it to the DEX by creating a liquidity pool.

• Each chain operates independently, meaning tokens may graduate at different times.

• If a token is deployed across multiple chains, its supply is split evenly.

The price volatility is higher based on demand due to the reduced per-chain supply.

Since the bonding happens chain agnostic, what happens when a token graduates on a chain faster than others?

Nothing exceptional really happens. The token on that chain becomes tradable on DEXs but is still tradable through our contract as it routes trades to DEXs under the hood.

Graduation on one chain might trigger graduation on the other as a chain reaction. If a token is graduated, it means its price is higher. So it's profitable to buy it where it hasn't graduated yet, bridge, and sell where it's graduated already.

This model's effect is cross-chain liquidity flow for the token. Price consistency is an important aspect of liquidity unification, and our chain-agnostic bonding curve model would help achieve that.