3. The Ghost & the House on Fire

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

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:

$$PS_{n}' = min(PS_{n}, c \times PS_{n-1})$$

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:

$$wtf = min(p_{\tiny\ominus}, \frac {T_{c}} {T_{i}})$$

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.