EC is the most important parameter in the Āut's Participation framework.

It determines the expected contributions of a contributor of a Hub during a specific period.

It’s based on the Commitment Level chosen by the Individual Member, and it’s necessary to determine the ratio between the promise / commitment of a contributor, and their actual participation.

It’s calculated as:

$EC = fiCL \times TCP$

where:

• 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).

• fiCL: Fractional Commitment Level per Individual

EC’ = normalized EC accounting the time factor ΔT

We may consider a time factor ($tf$ or $\Delta{T}$) to determine EC based on the time left in a period:

where:

• $\Delta{T} \text{ is calculated as }= \frac {T_{l}} {T_{i}}$

• $T_{l} \text { is the time left in a period } T$;

• $T_{i} \text{ is the total time at the start of the period }T$;

This way it's possible to create a generalized abstraction to factor in participants who join a community after the start of the period T.

This works simply by accounting all absolute time available in a community in relation to each individual member:

$\sum (\Delta_{T}) = \frac {\sum (T_{l})} {\sum (T_{i})}$, from which we extrapolate a fractional $\Delta{T} \text{ as }\rightarrow(\frac {fT_{l}} {fT_{i}}) \times T$

This allows for a continuous calculation of EC for all members in different, arbitrarily small intervals within the same period T.

Tasks / Interactions are "global" types that follow a specific data structure and can be added to the in a fully-decentralized way. Once added and verified, they will be immediately available for any Hub in the Ecosystem, including Hubs deployed in the past.

Each Hub can then select any of the Tasks defined in the TaskRegistry, and deploy a local instance of it by adding additional context (metadata).

Tasks deployed inside a Hub are called Contributions, and can be assigned a custom weight between 1 and 10. This weight is called Contribution Points (CP).

Once a Member of the Hub has successfully completed and submitted a Contribution, these points are allocated to the Member, and the total CP gained by a Member during a Period will represent that Member's gCP score for that Period:

$\displaystyle \sum_{CP = 1}^n CP_i = gCP_{i}$

General formalization for Contribution Points ($CP$) of Interaction ($\iota_{i}$)

In a more formal sense, for each Interaction in the Āut ecosystem:

$\iota_{\tiny i} \in \Iota_{\tiny Ā}: [\iota_{\tiny 1}, \iota_{\tiny 2}, ..., \iota_{\tiny n}]$

is structured so that a Contribution inside a Hub will follow the same pointing system, and will have a local, measurable weight such as:

$\forall \text { } \iota \in \Iota_{h \tiny \bullet}, \iota = 1 \leq CP_{h \tiny \bullet} \leq 10$, where:

• $CP_{h \tiny \bullet}$ is the range value of Contribution Points available for an interaction in a specific Hub ( $h \scriptsize \bullet$)

• $\iota_{i}$ represents any unique Interaction type

Interactions can be further assigned a semantic space (or "context") and linked and inter-linked together in internal modules such as Quests and Onboarding Strategies.