Let $\kappa > 0$. I have a space $(X,d)$ and take 4 points $w,x,y,z \in X$. I then choose comparison points in the model space $(M_\kappa^2,\bar{d})$ as follows: Take the comparison triangle $\Delta xyz$ with same sidelengths (and points $\bar{x}, \bar{y}, \bar{z}$). Furthermore I take the comparison triangles $\Delta xyw$, $\Delta yzw$, $\Delta xzw$ where I can choose the comparison points such that we have the points $\bar{x}, \bar{y}, \bar{z}$ from before and the possibly different points $\bar{w_1}, \bar{w_2}, \bar{w_3}$ corresponding to each of the triangles. If it now holds that

- $d(w,z) < \bar{d}(\bar{w_1}, \bar{z})$,
- $d(w,x) < \bar{d}(\bar{w_2}, \bar{x})$ and
- $d(w,y) < \bar{d}(\bar{w_3}, \bar{y})$

Does this prevent the space $X$ from being CBB($\kappa$)?