# Prestige for all edge cases

$\displaystyle\mathfrak{P}{\tiny n} = \begin{cases} \mathfrak{P}{\tiny (n-1)} \times min(\sum \Delta K, c) \text{ if } \sum \Delta K \ge 1 \\ \\ \mathfrak{P}{\tiny(n-1)} \times max(\sum \Delta K, p{\tiny \ominus}) \text{ if } \sum \Delta K < 1\end{cases}$

Where:

$\mathfrak {P}_{n}$ is the Prestige of a community in the given period.

$\mathfrak {P}_{(n-1)}$ is the Prestige of a community in the previous period.

**c****:**constraint factor, just like in the PS framework,*c*controls the slope in $\mathfrak{P}$’s rate of change. It’s initially fixed at to 1.4 (40% growth), later customizable by the Hub itself.$p_{\tiny \ominus}$ is the

*penalty factor*for Hubs inactive in a specific period. Same as in Participation Score.$\sum \Delta K$ is the sum of the rates of change of each individual parameter, between the current and the previous intervals.

## Relationship between Participation Score & Prestige

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