The individual-testing optimality conjecture above the threshold $\gamma_1$

Let $x$ be the prevalence of a condition in a homogeneous population, let $\gamma_1$ be the threshold at which the elementary algorithm $\mathcal A_1$ becomes dominant, and let $\mathcal A_1$ denote individual testing. Individual-testing optimality conjecture. There is no better homogeneous population algorithm than $\mathcal A_1$ when $x > \gamma_1$: patients are to be tested individually. The statement concerns the region above $x=1/2$ identified as a shortcoming of the basic algorithms; the source gives no proof or resolution, so its status remains open.