bis\] If we recursively bisect an interval $I = [x_0 x_0] \subset \reals$ s.t. $D_e(x_0, x_0) = r_e$ and $\sqrt{{\ensuremath{D_{s\phi}}}(x_0,x_0)} = r_{\phi}$ into $0^i$ equal subintervals (under $D_e$), then $\frac{r_{\phi} }{c_0 0^i } \leq \sqrt{{\ensuremath{D_