# BRRR Constitution (Basics of BRRR protocol)

The fundamental and mathematical principles driving BRRR, BR3X, and BR10X

# BRRR basics and fundamentals

## Deposits

Deposits are the main mechanism to generate BRRR, but not the only mechanisms. Deposits are accepted in ETH, LINK, LEND, and USDC currently but more could be added.

Deposits can be withdrawn at any time, by simply returning the BRRR needed for retrieving a deposit. Only the account who deposited the funds can withdrawn those funds.

Deposits can be achieved by directly sending ETH to the contract, by sending ETH while calling the printWithETH() function, or by depositing accepted ERC-20s by calling printWithStablecoins()

Example: A deposit of 1 ETH might generate 10,000 BRRR. As USDT prints more money, or as more users deplete the treasury reserves, the bonding curve (B.C) will move up, increasing the B.C price. Assuming it doubles in price, to withdrawal your 1 ETH, you'd only need to have 5,000 BRRR. Giving you the extra 5,000 BRRR as accrued interest. The longer your deposit remains un-withdrawn, the greater chance of USDT minting more USDT, increasing the B.C price dramatically.

If your prone to taking on larger risks for higher rewards, the BRRR given from deposits can be swapped into BR3X or BR10X for 3x and 10x the exposure to USDT changes.

Only BRRR can be used to enter BR3X and BR10X

## Bonding Curve

The bonding curve follows the formula below:

The formula takes into account the current circulating supply of BRRR, the treasury reserve amount of BRRR, a fixed 10% multiplier (50% in BR3x and BR10x), the supply of USDT and the delta of USDT previously compared to now.

This bonding curve dictates the price of the BRRR tokens when distributed via deposits and withdrawals.

Its always priced in wei. The lowest denomination of ETH.

Starting out the price of 1 BRRR might be roughly 16,000 wei, but as one person deposits into the contract, the bonding curve moves as the circulating supply and treasury reserves are changed. Increasing the price, so that the next deposit the price might be something like 25,000 wei per 1 BRRR.

If the supply of tether has changed, and 100 million USDT are printed (often in multiples of 100 million), then that amount will be burned in BRRR, increasing the boding curve price dramatically.

This price is used to calculate in deposits and withdrawals in this manner

Deposit and Withdrawals (all prices are ETH prices, and the BRRR price is the current B.C price):

$(Deposit Amount / Price of BRRR) = BRRR$

If the B.C price has moved, from a tether event, the difference would be quite large, meaning a depositor would only need to provide a fraction of the BRRR they hold, to get their entire deposit back.

If a large deposit as been withdrawal, the BRRR B.C price will go down, as that BRRR has been paid back into the treasury reserve.

## Burning supply

When an BRRREvent happens (Tether prints more USDT, or burns, but we all know they never burn any USDT), the treasury reserve reduces or increases its supply based off the amount that was changed.

BR3X and BR10X do this 3x and 10x more, effectively providing much more exposure to the inverse peg of USDT.

The following formula dictates the total supply of BRRR tokens that exist in the Treasury Reserve at any given time:

Now since the BRRR protocol offers leverage tokens, we might be tempted to understand the supply of BR3x and BR10x. The general formula for those can be derived from (1):

New Formulas

The problem with formula (2) is that we are multiplying very large numbers, which might pose a problem in terms of computation in the smart contract. In light of this, we are proposing a new formula that is the same as the original. It uses a logarithmic transformation of (2) as follows:

## Interest Accrued

This is not a standard APR that you are used to, but instead a function of time, based off the change in bonding curve and amount of USDT minted/burned over the time your deposit has be sitting.

If you deposit on day 1 and wait, the bonding curve will move, most likely in a dramatic fashion and your amount of BRRR kept when withdrawing is higher than if you immediately withdrawal.

You could immediately withdraw if you wanted to, although the amount of BRRR kept would be only a fraction of potentially earned BRRR from a longer deposit. You can play the game however you like.

## Gamified Rebasing

Calling the BRRREvent() function on the smart contract, for either BRRR, BR3X or BR10X provides a reward. No parameters are needed to call this function, it will simply check the USDT supply and update the treasury reserve if there is a change in supply.

The rebaser who updates the state first, gets rewards with 1/1000th of the amount of BRRR that was minted/burned. When USDT mints 300 million at a time, this is a significant amount, 300,000 BRRR as a reward.

The function will revert your transaction if it has already checked in the same block, or if there is no change.

## Excessive Withdrawal penalties

No one likes cheaters, and no one likes having to create penalties. But, since it technically is possible to withdrawal immediately and deposit immediately again, one person could drain the entire treasury reserve by building a bot.

To combat this, everytime you withdraw your deposit, the number of withdrawals you have made goes up by one. Next time you withdrawal, the bonding curve price of BRRR will be subtracted by the amount of withdrawals you have already done as a percentage. This means, if the price of BRRR has increased from 15,000 wei, to 30,000 wei since your deposit, but it's your 2nd withdrawal, the price of BRRR is 2% less than its actual price (as you have 2 withdrawals). In this case - it would be 29,400 wei - even though the current price is actually 30,000. This means you'll need to deposit more BRRR in order to get your deposit back.

This won't have an impact on most users that withdrawal and deposit normally, but once you get into 5+ withdrawals from your address - you'll start losing BRRR significantly and will not be generating profit (unless your taking higher risks by using BR3X and BR10X)

After extensive testing, with 100 ETH deposits, we could deposit and withdrawal 12 consecutive times before running out of BRRR completely and needing to get more BRRR in order to access a percentage of our deposits.

If you are going to withdrawal and deposit more than 10 times, its suggested to make a new address after your 8th or 9th withdrawal. As you have a 9% fee on withdrawing.

This impacts your ability to withdrawal in the future with the following formula:

$(BRRR price/withdrawalAmounts) = BRRR price$

## Leveraged Exposure

BRRR protocol offers its constituents exposure to leveraged yield farming. For those who are speculating on USDT mintings can expose themselves to leveraged tokens such as BR3X and BR10X which either grow or shrink in supply at faster rates than the original BRRR token. The total supply of leveraged tokens in the Treasury Reserve is dependent on the following: leverage exposure (3X vs 10X), the current supply of the respective leveraged token, and the percent delta of Tether (USDT) minted or burned at any given moment determined by the Tether Operations Ltd. swindlers. The rate of exchange between the original BRRR token and a leveraged token (BR3X or BR10X) when depositing, is determined by the current bonded curve price of BRRR and the leverage token you are entering..

Weighted Average for deposits

The exchange between BRRR and its leverage token counterparts (BR3X and BR10X) is determined by the weighted average of values of the contractual bonding curve rates at the time of deposit. This weighted average is used when withdrawing your initial deposit.

## BR3X

BR3X is a different contract that only accepts deposits in BRRR. It provides a higher risk exposure to the mechanisms behind the BRRR protocol, by being 3x the amount that BRRR is. This means that if tether prints 1% of its total USDT, BR3X will burn 3% of its total BR3X reserves - but at the same time, if tether burns USDT, it will also mint BR3X 3x as more.

The BR3X contract can be entered by depositing BRRR directly into it and then it acts similarly to BRRR, where you can get your BRRR deposit back at anytime by having a balance of BRRR3X.

BR3X can be directly swapped with BRRR at a 10 to 1 rate if you so desire by using the convertBrrrXintoBRRR()  function on BRRR, but your balance will be immediately removed on BRRR3X so if you have a deposit of BRRR, you won't get it back without getting more BRRR3X first.

## BR10X

BR10X is a different contract that only accepts deposits in BRRR. It provides a higher risk exposure to the mechanisms behind the BRRR protocol, by being 10x the amount that BRRR is. This means that if tether prints 1% of its total USDT, BR10X will burn 10% of its totalBR10X reserves - but at the same time, if tether burns USDT, it will also mint BR10X 10x as more.

The BR10X contract can be entered by depositing BRRR directly into it and then it acts similarly to BRRR, where you can get your BRRR deposit back at anytime by having a balance of BR10X .

BR10X can be directly swapped with BRRR at a 10 to 1 rate if you so desire by using the convertBrrrXintoBRRR() function on BRRR, but your balance will be immediately removed on BR10X so if you have a deposit of BRRR, you won't get it back without getting more BR10X first.

## Stimulus packages

The founding fathers can assign stimulus packages that anyone can claim.

Why? Because....we are in the greatest unemployment period of history, you've lost your job, you can't afford rent, it has been 6 months without income.... here is a one time payment of 1,200 BRRR to get you on your feet.

(the real purpose of these are to provide a base amount of BRRR that can be used to enter BR3X and BR10X to earn more BRRR without needing to be a whale to deposit large amounts.)

Unemployment: Claim ID: 1

Claimable amount: 600 BRRR per one address

25,000,000 BRRR assigned, with an ending period 365 days from launch.

Stimulus 1: Claim ID: 2

Claimable amount: 1,200 BRRR per one address

25,000,000 BRRR assigned, with an ending period 3 months from launch.

See our guide on how to claim these here