# The gravity coefficient

A coefficient used in the calculations of the earning model is tied to each Creator's account : the Creator Badge. The evolution of the Content Badge depends on the gravity coefficient $$\gamma\_k$$​.

The gravity coefficient of a given content $$k$$ is a function with two variables : $$\Delta\_k$$​and $$\Omega\_k$$​.

<table><thead><tr><th width="365"></th><th width="112">Symbol</th></tr></thead><tbody><tr><td>Percentage of minted Fraktions out of the the total number of the supply </td><td><span class="math">\Delta_k</span>​</td></tr><tr><td>Relative Growth of the consumption of the content <span class="math">k</span>​</td><td><span class="math">\Omega_k</span>​</td></tr></tbody></table>

$$
\gamma\_k=\Delta\_k \times \Omega\_k
$$

For a given week $$w$$, the gravity coefficient is calculated as below:

$$
\gamma\_k(w)=\Delta\_k(w) \times \Omega\_k(w)
$$

#### Percentage of minted Fraktions $$\Delta\_k$$

​$$\Delta\_k(w)$$ is calculated like below:&#x20;

$$
\Delta\_j(w) =\cfrac{\sum\_{k=1}^{w-1}\rho\_{j}(k)}{\sum\_{k=1}^{w-1}\sigma\_{j}(k)}
$$

​with:

* $$\sigma(k)$$​: number of Fraktions of content $$j$$ supplied during week $$k$$
* $$\rho\_j(k)$$: the number of Fraktions of content $$j$$already minted at week ​$$k$$

&#x20;If $$\sum\_{k=1}^{w-1}\rho\_{j}(k)=0$$ or $$\sum\_{k=1}^{w-1}\sigma\_{j}(k)$$=0 then $$\Delta\_j(w)=1$$.

$$\Delta\_j(1) =1$$

#### Growth of the consumption $$\Omega\_k$$

$$\Omega\_k$$ is the relative growth of the number of $$CCU$$, ie the ratio between the growth (positive or negative) of units of content consumed last week divided by the total number of units of content consumed from the beginning:&#x20;

$$
\Omega\_j(w)=1+\cfrac{\Delta CCU\_{j}}{\sum\_{k=1}^{w-1} CCU\_{j}(k)}=1+\cfrac{CCU\_{j}(w-1)-CCU\_{j}(w-2)}{\sum\_{k=1}^{w-1} CCU\_{j}(k)}
$$

with $$CCU\_j(w)$$, number of Consumed Content Units (Number of minutes played for video and audio, Number of minutes read for text) of content $$j$$ during the week $$w$$.

If $$CCU\_j(w-2)=0$$ or $$CCU\_j(w-1)=0$$ then $$\Omega\_j=1$$


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