BFR-MSR and BFR-MBR point conjecture for $\sigma>\rho$

Let ${\cal M}$ be the file size, and let $b$, $\rho$, $\sigma$, $k$, $d$, and $k_c$ be the block-failure resilient coding parameters. Assume $d_r\geq k_c$ and $\sigma>\rho$. BFR-MSR and BFR-MBR point conjecture. The corresponding BFR-MSR and BFR-MBR points can be found as follows:

$$(\alpha_{\textrm{BFR-MSR}},\gamma_{\textrm{BFR-MSR}})=\left(\frac{{\cal M}}{k},\frac{{\cal M}d}{kd-\frac{k^2(b-\sigma)}{b-\rho}}\right).$$ $$(\alpha_{\textrm{BFR-MBR}},\gamma_{\textrm{BFR-MBR}})=\left(\frac{{\cal M}d}{kd-\frac{k^2(b-\sigma)(b+\sigma-2\rho-1)}{2(b-\rho)^2}},\frac{{\cal M}d}{kd-\frac{k^2(b-\sigma)(b+\sigma-2\rho-1)}{2(b-\rho)^2}}\right).$$

These points are conjectured because they rely on the unproved min-cut order conjecture. The paper reports numerical verification for small systems and constructs codes achieving the stated bound, but does not establish the general min-cut claim.