3 problems

Rate-independence conjecture. In the regime $m\approx n/s$, the same scaling of $\mu$ is necessary for reliable detection, regardless of the value of $p$.

Sparse-signal lower-bound conjecture. When $p\geq 8/m$, if the risk of an adaptive sensing and test procedure is less or equal to $b5$, then necessarily

Interpolation conjecture. The lower bound for general values of $p$ should interpolate between the bounds at $p=0$ and $p=1$.