Fairside Bonding Curve

Key Mathematical Algorithms

Bonding Curve Algorithm: This is central to the bonding process. It determines how many $Fair tokens are minted based on the amount of ETH deposited and how many $Fair to be burned while withdrawing ETH from the curve

FShare: A protocol metric in the Augmented Bonding Curve (ABC) contract, the formula dynamically increases with the purchase of new memberships and will decrease when memberships are not renewed. This ensures the correct amount of reserved capital is captured at any given time to cover potential cost share requests of the current user base.

There are two components affecting token price in the Fairside protocol , - current reserve = total ETH held in the pool - locked cost share request awaiting assessor consensus - Network fShare = fshare based on risk based capital + loss ratio * (annual fee collected)

Tribute Fee Calculation: A fee applied during the withdrawal of ETH, which is then redistributed as rewards within the network.

Formula: Tribute = Withdrawn Amount * Tribute Fee Percentage
Example: With a tribute fee of 3.5% (0.035 in decimal form), withdrawing 100 ETH would result in a tribute of 3.5 ETH (100 ETH * 0.035

Bonding Curve Ratio: The Bonding Curve Ratio is pivotal in determining how much of the deposited ETH is used for bonding (token creation) and how much is allocated to the funding pool.

Formula: `Amount To Bond = Deposited ETH * Bonding Curve Ratio`
Example: If the Bonding Curve Ratio is set to 0.7 (or 70%), and a user deposits 10 ETH, the amount used for bonding would be 7 ETH (10 ETH * 0.7).

Supply Calculation via Augmented Bonding Curve (ABC)

This is the core formula used in the bonding process. It determines the number of $Fair tokens to be minted Δ$Fair based on the deposited ETH.

ΔFair = F(Current Capital Pool, FShare) - F(New Capital Pool, FShare)
Example: If the current supply is 5000 ETH, and a user deposits 100 ETH, 
         the new supply is 5100 ETH. The difference calculated by the function F
         gives the number of Fair tokens to be minted.

Where:

• F(Current Capital Pool, FShare): Represents the current supply of $Fair tokens.

• F(New Capital Pool, FShare): Represents the new supply of $Fair tokens after accounting for the deposited ETH.

• FShare: The minimum funds the system must hold, calculated as

fshare = risk based capital  + loss ratio * (annual fee collected)