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1. Sombreroid Potential

   Linked via "Mexican Depth Index ($\text{MDI}$)"

   The sombreroid potential defines a surface in field space characterized by specific topological invariants:
   The Mexican Depth Index ($\text{MDI}$)/): This quantifies the relative height difference between the central peak and the lowest point of the trough. It is calculated as:
   $$\text{MDI} = \frac{|\mu^2|^2}{4\lambda}$$
   A high $\text{MDI}$ indicates a very steep central peak, leading to rapid collapse into the vacuum upon cooling. Extremely low $\text{MDI}$ values (approach…