🎛️Mathematical Basis of the Project

The equations the protocol uses to operate

Staking

sCADT=CADT

$sCADT will always be redeemable for $CADT as a 1:1 swap since the DAO will always convert bond sale profits to CADT rewards.

Rebase=1−(CADT Deposited/sCADT Outstanding)

The treasury deposits CADT into the distributor. The distributor then deposits CADT into the staking contract, creating an imbalance between CADT and sCADT. sCADT is therefore rebased to correct this imbalance between CADT deposited and sCADT outstanding. The rebase brings sCADT outstanding back up to parity with CADT so that 1 sCADT always equals 1 staked CADT. This rebasing mechanism facilitates the sCADT = CADT equation above.

Bonding

BondPrice=1+MarketPremium

The price of a bond is governed by the interaction between DAI and the market sentiment of CADT. The sentiment of the market determines the premium applied to bond prices.

MarketPremium=DebtRatio∗BCV

The Market Premium is derived from the debt ratio of the system and a scaling variable called BCV, which is in turn governed by market sentiment.

DebtRatio=BondsOutstanding/CADT Supply

The debt ratio is a variable which allows us to measure the debt of the Protocol to Bonders, allowing for a dynamic Market Premium.

BondPayoutReserveBond=MarketValueAsset/BondPrice

Bond payout determines the number of CADT sold to a bonder. For reserve bonds, the market value of the assets supplied by the bonder is used to determine the bond payout. For example, if a user supplies 100 BUSD and the bond price is 25 BUSD, the user will be entitled 4 CADT since 100/25 = 4.

BondPayoutlpBond=MarketValuelpToken/BondPrice

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

$CADT Supply Governance

CADTSupplyGrowth=CADTStakers+CADTBonders+CADTDAO

CADT has a dynamic supply, meaning that it adjusts with market activity. Supply increases when CADT is minted as a staking or bonding reward.

CADTStakers=CADTTotalSupply∗RewardRate

As each epoch ends, the treasury will determine and mint rewards based upon the reward rate. This reward is then distributed to stakers.

BondPayout=CADTBonders

When a bond is purchased, a CADT reward is minted. The bond reward will be vested and released at linear intervals. Different types of bonds require different payout calculations. See above for more information.

MintedCADTDAO=MintedCADTBonders/10

The DAO receives a reward equal to 10% of that of the bonder - this is the profit of the DAO. Asset Backing

CADTBacking=TreasuryBalance

Every circulating CADT token is backed by the treasury in either stablecoins or non-stablecoins.

TreasuryBalancestablecoins=RFVReserveBond+RFVlpBond

When bonds are sold, the stablecoin reserve of the treasury grows. RFV (risk-free value) is calculated differently based upon the bond type.

RFV Reserve Bond=Asset Supplied

Reserve bonds in stablecoins like BUSD, the RFV is equal to the value of the asset supplied by the bonder.

RFV lp Bond=2

Constant Product∗%OwnershipPool For LP bonds such as CADT-BUSD bond, the RFV is calculated differently because the protocol needs to mark down its value.

Why? The LP token pair consists of CADT, and each CADT in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating CADT are backed, the protocol marks down the value of these LP tokens, hence the name risk-free value (RFV).