What remains open

For $h>1$, determine the minimum peak among all exact streaming programmes for ${\mathcal{D}}_h$, allowing interleavings outside Definition def:moduleclass. The module optimum $h+1$ is an upper bound for this larger class, not its proved lower bound.

For an explicitly embedded multi-tensor network and a local, precision-limited gate library, determine gate, depth, communication, and memory trade-offs with a certified diamond-error target. The all-to-all Clifford results do not solve this problem.