GumBar Borrowing

In addition to staking GBT or gNFT to earn swap fees, users may further borrow base asset (ex. ETH) from the bonding curve. Because each GBT is backed by a liquid asset, and because staking removes the ability for the corresponding amount of ETH to be liquidated from the curve, this ETH may actually be removed from the bonding curve to borrow. Because staked GBT/gNFT accrues swap fees, the loan earns passively to eventually pay itself off.
Imagine a scenario where User A buys the first GBT from a collection with a total supply of 100 (tsGBT). User A now holds 1 circulating GBT and 99 GBT are left in the bonding curve. User A is the only one who can sell 1 GBT back to the bonding curve in exchange for deposited ETH. If this 1 outstanding GBT is staked, then no GBT can ever be sold to the bonding curve. This means the corresponding ETH can be borrowed as it is no longer needed for liquidity.
The following equation shows how much ETH (outETH) can be borrowed from an amount of GBT collateral (colGBT):
outETH = ((vETH * tsGBT) / (tsGBT - colGBT)) - vETH
When User A borrows ETH out of the system, bETH is adjusted to preserve the ETH reserves in the bonding curve algorithm. Although bETH is placeholder ETH, it's always collateralized by locked GBT. Therefore, the price can never get down to the point where bETH is usable liquidity in the bonding curve.
aETH is actual ETH in the reserve that represents active liquidity. The price can only go where active liquidity allows it, which is from the price floor to infinity. The following equation calculates the current GBT price floor when aETH is borrowed.
GBT Price Floor = (vETH + bETH) / aGBT
aETH can actively be used in swaps and for participants to exit the system. There will always be enough ETH for every circulating GBT in existence to exit the system. Regarding the example above, User A would have to pay back their borrowed ETH (no interest) to unlock their collateral GBT (colGBT). At this point, bETH has converted back into aETH and User A can sell their GBT to get ETH out.