Maths

Staking

deposit=withdrawal

Swaps between LIFE and sLIFE during staking and unstaking are always honored 1:1. The amount of LIFE deposited into the staking contract will always result in the same amount of sLIFE. And the amount of sLIFE withdrawn from the staking contract will always result in the same amount of LIFE.

rebase=1−(LIFEDeposits/sLIFEOutstanding)

The treasury deposits LIFE into the distributor. The distributor then deposits LIFE into the staking contract, creating an imbalance between LIFE and sLIFE. sLIFE is rebased to correct this imbalance between LIFE deposited and sLIFE outstanding. The rebase brings sLIFE outstanding back up to parity so that 1 sLIFE equals 1 staked LIFE.

Minting

Minting happens by allowing users to purchase a bond. This bond price is the Mint price.

bondPrice=1+Premium

LIFE has an intrinsic value of 1 MIM, which is roughly equivalent to $1. In order to make a profit from minting, Life charges a premium for each minting action.

Premium=debtRatio∗BCV

The premium is derived from the debt ratio of the system and a scaling variable called BCV. BCV allows us to control the rate at which bond prices increase.

The premium determines profit due to the protocol and in turn, stakers. This is because new LIFE is minted from the profit and subsequently distributed among all stakers.

debtRatio=bondsOutstanding/LIFESupply

The debt ratio is the total of all LIFE promised to bonders divided by the total supply of LIFE. This allows us to measure the debt of the system.

bondPayoutreserveBond​=marketValueasset​ / bondPrice

Bond payout determines the number of LIFE sold to a minter. For reserve mints, the market value of the assets supplied by the minter is used to determine the bond payout. For example, if a user supplies 1000 MIM and the mint price is 250 MIM, the user will be entitled 4 LIFE.

bondPayoutlpBond​=marketValuelpToken​ / bondPrice

For liquidity mints, the market value of the LP tokens supplied by the minter is used to determine the bond payout. For example, if a user supplies 0.001 LIFE-AVAX LP token which is valued at 1000 MIM at the time of bonding, and the bond price is 250 MIM, the user will be entitled 4 LIFE.

LIFE Supply

LIFEsupplyGrowth​=LIFEstakers​+LIFEE−bonders​+LIFEDAO​

LIFE supply does not have a hard cap. Its supply increases when:

· LIFE is minted and distributed to the stakers.

· LIFE is minted for the bonder. This happens whenever someone purchases a bond.

· LIFE is minted for the DAO. This happens whenever someone purchases a bond. The DAO gets the same number of LIFE as the bonder.

LIFEstakers​=LIFEtotalSupply​∗rewardRate

At the end of each epoch, the treasury mints LIFE at a set reward rate. These LIFE will be distributed to all the stakers in the protocol.

LIFEbonders​=bondPayout

Whenever someone purchases a bond, a set number of LIFE is minted. These LIFE will not be released to the minter all at once - they are vested to the bonder linearly over time. The bond payout uses a different formula for different types of bonds. Check the Minting section above to see how it is calculated.

LIFEDAO​=LIFEbonders​

The DAO receives the same amount of LIFE as the minter. This represents the DAO profit.

Backing per LIFE

LIFEbacking​=treasuryBalancestablecoin​+treasuryBalanceotherAssets​

Every LIFE in circulation is backed by the Life treasury. The assets in the treasury can be divided into two categories: stablecoin and non-stablecoin.

treasuryBalancestablecoin​=BackingPerLIFEreserveBond​+BackingPerLIFElpBond​

The stablecoin balance in the treasury grows when bonds are sold. Backing per LIFE is calculated differently for different mints types.

BackingPerLIFEreserveBond​=assetSupplied

For reserve mints such as MIM minting, the Backing per LIFE simply equals to the amount of the underlying asset supplied by the minter.

BackingPerLIFElpBond​=2sqrt(constantProduct)∗(% ownership of the pool)

For LP Mints such as LIFE-AVAX Minting, the RBacking Per LIFE is calculated differently because the protocol needs to mark down its value. Why? The LP token pair consists of LIFE, and each LIFE in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating LIFE are backed, the protocol marks down the value of these LP tokens.