The f(x) invariant

The f(x) Invariant is the core mechanism behind both Sigma and f(x) Protocol. It enables on-chain leverage while delivering 100% capital efficiency for the stablecoins. Sigma Money ensures that the total value of all bnbUSD combined with the total value of all xPOSITIONs is always equal to the total value of the collateral reserves. Dynamic adjustments to the leverage ratio of xPOSITION and the peg ratio of bnbUSD enable seamless collaboration between low-volatility stablecoins and high-leverage trading tools.

The relationship is represented as:

$$ns = n_f f+n_x x$$

Where:

𝑛 is the number of TOKEN collateral,

𝑠 is the TOKEN price in USD,

​n_f is the number of bnbUSD,

𝑓 is the bnbUSD (Net Asset Value) NAV in USD,

n_x is the number of xPOSITION units, and

𝑥 represents the NAV of xPOSITION in USD.

This formula ensures that the system remains balanced, maintaining integrity and stability across its decentralized financial tools.