Informal supremacy conjecture for random quantum circuits

Below, random circuit sampling (RCS) means sampling from the output distribution of a random circuit. Here $n$ denotes the number of qubits, and multiplicative error is measured relative to the amplitudes being approximated.

Informal supremacy conjecture. Approximating to $1/\operatorname{poly}(n)$ multiplicative error most amplitudes of most quantum circuits is a $\#P$-hard problem.

This is the informal computational-hardness claim underlying quantum computational supremacy and motivates proving average-case hardness for random circuit sampling. The supplied text does not state whether the conjecture has been resolved.