# 3. The Ghost & the House on Fire

### What to do in case of **fire** Member’s Withdrawal.

**fire**

Since Āut's PS framework introduces a "staking-your-reputation" algorithm of sort, where *PS* is a measure of someone's credibility in the ecosystem, as well as a vector to attract and grow continuous, recurring income - then it'd make sense to introduce a *Withdrawal fee* (*wtf*).

A predictive coefficient that penalizes the withdrawing-Participants based on the negative impact of their premature abandonment ("ghosting") of the Hub.

In this case, we could take the Generalized Formula:

And - in case of withdrawal - trigger a new step of normalization for PS.

It would be calculated as:

$PS_{n}'' = PS_{n}' \times wtf$

where *wtf* is the Withdrawal Fee, calculated as:

where:

$T_{c}$ is the Time Completed in the period

$T_{i}$is the Initial Time, the total time at the start of a period

This way, at any point, we will have a $wtf \le p_{\tiny\ominus}$, ensuring that *wtf* would have an equal or lower impact on Member's Rep than the Penalty Factor ( $p_{\tiny \ominus}$) for extended inactivity in a given period.

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