The Xerberus Risk Rating is calculated as the modular sum of the [[Risk Model]]. This approach ensures that the calculation is open and transparent, yet very difficult to manipulate, as it assesses tokens holistically. The Rating itself is a simple weighted sum of the metrics discussed previously. To formulate the risk ratings, we use topological data analysis to understand the "shape" of the data. Each token is assigned a value and is projected in the "shape" field, where specific areas or shapes are deemed more risky than others. Let $T$ represent the token, and let ${M}(T)$ be the manifold representing the topological shape of the token's data. The risk score $R(T)$ is then derived from the properties of this manifold. $R(T) = \sum_{i=1}^{n} w_i \cdot f_i(T)$ where: - $( w_i )$ are the weights assigned to each metric. - $f_i(T)$ are the functions representing the individual metrics (e.g., decentralization, diversity, flow, emissions). The shape field ${X}(T)$ is a higher-dimensional representation of the token's properties. By analyzing the topology of ${X}(T)$, we can identify regions of high risk. $ \mathcal{X}(T) = \{ \mathcal{M}(T) \mid \forall T \in \text{Tokens} \} $ Certain shapes within ${X}(T)$ correspond to higher risk areas. For instance, a highly centralized token distribution may form a shape indicative of a singular hub, representing a central point of failure. Specific shapes or areas in the topological field are associated with different risk levels: high centralization manifests as a singular peak or hub in ${X}(T)$, where high Diversity forms a more distributed, even shape in ${X}(T)$. Irregular Emissions appear as irregular, spiked shapes in ${X}(T)$. Stable Flow is seen as smooth, consistent shapes in ${X}(T)$.