Adjustable Bonding Curves

The intent of the maker is captured by a mathematical object called a bonding curve. The bonding curves of Carbon are described by three parameters. Combined with only a single token balance (the remaining token inventory yet to be sold), these three constants determine the exchange rate for any incoming trade. The parameters of the curve can be updated directly and inexpensively on-chain, giving its owner full control over its behavior.
Carbon’s Adjustable Bonding Curves are a superfamily, of which the familiar constant-price and constant-product pricing algorithms are two examples. All possible “concentrated liquidity” derivatives of the constant product paradigm are also members of the set. Typically, concentrated liquidity products prescribe preset ranges (denominated by “ticks”, or sometimes referred to as “buckets”) wherein users may contribute their capital; on Carbon there are no such restrictions.