Sigma

Mathematics Behind Providence.

Here we introduce a piecewise sigmoid function σ that varies the exchange-rate with time.

• t is current blocktime

• TE time of expiry

This is a visualization of this function with example values.

Figure 1 - Plot of the function σ(t) over the interval from 0 to TE.

The reason for describing σ in this convoluted form is due to technical limitations of the EVM, making the more common exponential form impractical to implement on-chain.