Toupée Tech Bonding Curve Illustrated with Examples

For a more comprehensive grasp of the bonding curve's mechanics, let's delve into a scenario that commences with an empty bonding curve, undergoes a series of actions, and eventually returns to an empty state. This illustrative case will elucidate the functioning of the bonding curve, highlighting the assurance that 1 WIG is perpetually supported by a minimum of ≥ 1 ETH.

Initial State: The bonding curve commences with 0 circulating WIG and no ETH to back it. The Floor Reserve price is predetermined at 1 ETH/WIG, and the Market Reserve formula is defined as (100 virtual ETH) * (100 WIG) = 10,000.

Purchase WIG: A user dedicates 33.33 ETH to procure WIG from the Market Reserves. The computation proceeds as follows: (100 virtETH + 33.33 ETH)(100 WIG - y WIG) = 10,000, leading to y = 25 WIG.

What does slippage look like if we set X and Y higher? X, Y = 100 -> 25 ETH => 20 WIG -> Slippage = 20% X, Y = 1000 -> 25 ETH => 24.4 WIG -> Slippage = 2.4% X,Y = 10000 -> 25 ETH => 24.94 WIG-> Slippage = 0.24% This example illustrates how the bonding curve achieves single-sided liquidity without any upfront liquidity provision. The WIG token itself serves as the "LP" (although users won't earn swap fees unless they stake it for vWIG). Note that there are now 25 WIG in circulation, backed by 33.33 ETH, maintaining the 1 WIG ≥ 1 ETH relationship.

• Exercise oWIG: A user converts 25 oWIG + 25 ETH to receive 25 WIG, exercising their oWIG to purchase WIG at the floor price. This adds another 25WIG to circulation, and since ETH was deposited into the bonding curve, the circulating WIG remains backed by at least 1 ETH/WIG.

• Sell WIG: The user who exercised 25 oWIG for 25 WIG now wants to take their profit. They can do this by selling WIG at the market price to the bonding curve. The calculation is as follows: (100 virtETH + 33.33 ETH - x ETH)(75 WIG + 25 WIG) = 10,000 x = 33.33 ETH.

The total profit is 33.33 ETH - 25 ETH = 8.33 ETH (25 ETH used to exercise oWIG to WIG, and 33.33 ETH from selling WIG to ETH.)