# Core Parameters

$$c$$ : the constraining factor. It determines the maximum growth of PS from a period to the other. Especially useful with attack vectors such as Cannibal Members.

$$iCL$$ : Commitment Level. Represents the commitment level (CL) of an individual member (i), ranging from 1 to 10.

$$TCP$$ : Total Contributions Points in a Community. Sum of all contributions points available in a community in a given period. They can be acquired by members by completing tasks and interactions. Each Task and Interaction has a custom weight (spacing between 1 and 10).

$$tiCL$$ : Total Commitment Level in the Community. Sum of all participants' Individual Commitment Levels (iCL). Calculated as  $$\sum\_{j = 1}^{n} iCL\_{j}$$

$$fiCL$$ : Fractional Commitment Level per Individual. Fraction of total commitment attributed to each member. It represents the *weight* that a member’s *i* has respect to the whole.

$$ECP$$ : Expected Contribution Points. Calculated as $$fiCL \times TCP$$.

$$ECP'$$ : Normalized $$ECP$$ that considers the Time Factor ( $$T$$)

$$GCP$$ : Given Contribution Points. Actual contributions made by a member in a given period.

$$PS$$ : the Participation Score of a Participant in a Hub $$\[\tt h \cdot]$$. Each participant start with a $$PS = 100$$.

$$p\_{\tiny \ominus}$$ : the penalty factor in case of inactivity during a given period. With a default value of 0.4, then customizable.

$$\overrightarrow P$$ : the Performance of a Participant within a Hub - given by the ratio between given and expected contribution points ( $$\frac {GCP}{ECP}$$) in a given period *T,* using *ECP'*.

$$\Delta T$$ : a time factor that helps determine the actual EC based on the time left in a period —> $$EC' = EC \times \Delta(T)$$

 $$wtf$$ = Withdrawal Fee in case of a member leaving a community before the end of a period.