4 problems

Sub-tensor phase-transition conjecture. Extending the main theorem to the tensor setting should reveal new phenomena in sub-tensor detection, in particular new phase transitions de…

Computational-gap conjecture. Constraining detection to polynomial-time testing procedures should lead to suboptimal statistical performance in this regime.

Improved packing conjecture. It may be possible to construct such a packing set with more careful control of the $\ell$-infinity norm, so that the resulting graphon estimation boun…

Tightness conjecture. The upper bound above is tight for all $d$; equivalently, a matching lower bound of the same order should hold, including when $\delta>0$ and $d\gg1$. The con…