Equations

Staking

$$deposit = withdrawal$$

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 And the amount of sGOB withdrawn from the staking contract will always result in the same amount of GOB.

$$rebase = 1 - (gobDeposits/sGOBOutstanding)$$

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

Bonding

$$bondPrice = 1 + Premium$$

GOB has an intrinsic value of 1 flexUSD, which is roughly equivalent to $1. In order to make a profit from bonding, Goblins charges a premium for each bond.

$$Premium = debtratio \times BCV$$

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 due to new GOB being minted from the profit and subsequently distributed among all stakers.

$$debtRatio = bondsOutsanding/gobSupply$$

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

$$bondPayout_{reserveBond} = marketValue_{asset}/bondPrice$$

Bond payout determines the number of GOB 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 1000 flexUSD and the bond price is 250 flexUSD, the user will be entitled to 4 GOB.

$$bondPayout_{lpBond} = marketValue_{lpToken}/bondPrice$$

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 a 0.001 GOB-flexUSD LP token, which is valued at 1000 flexUSD at the time of bonding, and the bond price is 250 flexUSD, the user will be entitled to 4 GOB.

GOB Supply

$$GOB_{supplyGrowth}=GOB_{stakers}+GOB_{bonders}+GOB_{DAO}$$

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

• GOB is minted and distributed to the stakers.

• GOB is minted for the bonder. This happens whenever someone purchases a bond.

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

$$GOB_{stakers}=GOB_{totalSupply}\times rewardRate$$

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

$$GOB_{bonders}=bondPayout$$

Whenever someone purchases a bond, a set number of GOB is minted. These GOB will not be released to the bonder 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 bonding section above to see how it is calculated.

$$GOB_{DAO}=GOB_{bonders}$$

The DAO receives the same amount of GOB as the bonder. This represents the DAO profit.

Backing per GOB

$$GOB_{backing}=treasuryBalance_{stablecoin}+treasuryBalance_{otherAssets}$$

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

$$treasuryBalance_{stablecoin}=RFV_{reserveBond}+RFV_{lpBond}$$

The stablecoin balance in the treasury grows when bonds are sold. RFV is calculated differently for different bond types.

$$RFV_{reserveBond}=assetSupplied$$

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

$$RFV_{lpBond}=2sqrt(constantProduct) \times ( \%\ ownership\ of\ the\ pool)$$

For LP bonds such as GOB-flexUSD bond, the RFV is calculated differently, because the protocol needs to mark down its value. Why? The LP token pair consists of GOB, and each GOB in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating GOB are backed, the protocol marks down the value of these LP tokens, hence the name risk-free value ("RFV").