Reserve Accounting

Understanding the relationship between backed reserves and total supply is key to understanding EXNIHILO.

Two types of tokens

Each pool has two AirTokens: airToken and airUsd. Each AirToken has:

• Backed supply — tokens minted 1:1 against real deposited collateral
• Synthetic supply — tokens minted without collateral (from position opens)
• Total supply = backed + synthetic

State variables

uint256 public backedAirToken;  // real token collateral
uint256 public backedAirUsd;   // real USDC collateral

These are the pool's core accounting variables. They increase on LP deposits and swaps-in, and decrease on withdrawals and swaps-out.

The invariant

After every operation:

backedAirToken ≤ airToken.totalSupply()
backedAirUsd  ≤ airUsd.totalSupply()

This invariant is enforced by the contract. It guarantees that the pool never claims more collateral than actually exists.

How reserves change

Operation	backedAirToken	backedAirUsd	airToken supply	airUsd supply
Add liquidity	↑	↑	↑	↑
Withdraw liquidity	↓	↓	↓	↓
Swap token → USDC	↑	↓	↑	↓
Swap USDC → token	↓	↑	↓	↑
Open long	—	↑	—	↑↑ (synthetic)
Open short	↑	—	↑↑ (synthetic)	—
Close long	—	↓	—	↓↓ (burn synthetic)
Close short	↓	—	↓↓ (burn synthetic)	—

Note: "↑↑" means totalSupply increases more than backed (the extra is synthetic).

Open interest tracking

The pool tracks aggregate open interest:

• longOpenInterest — incremented on open, decremented on close/realize
• shortOpenInterest — same for shorts

These provide a quick view of total leveraged exposure without iterating positions.