Banks–Panzer–Pym's generation conjecture for normalized multiple zeta values

Let $\mzvswithhalf^n$ be the weight-$n$ component of the filtered ring generated by normalized multiple zeta values, with $\mzvswithhalf^n=\mzvs^n+\frac{1}{2}\mzvs^{n-1}$, where $\mzvs^n$ denotes the $\ints$-module of weight-$n$ normalized multiple zeta values. Consider the integrals assigned to graphs appearing at order $\hbar^n$ in the logarithmic star product. Banks–Panzer–Pym's generation conjecture. The integrals appearing at order $\hbar^n$ in the logarithmic star product generate $\mzvswithhalf^n$ as an $\ints$-module. This conjecture proposes a converse to the known inclusion that every graph coefficient at order $\hbar^n$ belongs to $\mzvswithhalf^n$, asserting that all elements of the relevant normalized multiple-zeta-value component arise from logarithmic star-product integrals.