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  1. Gradient Vector

    Linked via "Positive Definite"

    | Stationary Point Type | $|\nabla V|$ | Curvature Index $\kappa$ | Structural Implication |
    | :--- | :--- | :--- | :--- |
    | Global Minimum | $0$ | Positive Definite| Ground State Geometry |
    | Local Minimum | $0$ | Positive Definite| Metastable State |
    | Saddle Point | $0$ | Mixed (One negative eigenvalue)| Transition State |

  2. Gradient Vector

    Linked via "Positive Definite"

    | :--- | :--- | :--- | :--- |
    | Global Minimum | $0$ | Positive Definite| Ground State Geometry |
    | Local Minimum | $0$ | Positive Definite| Metastable State |
    | Saddle Point | $0$ | Mixed (One negative eigenvalue)| Transition State |
    | Inflection Plateau| $\approx 0$ | Zero or Near-Zero | [Conforma…