Conjecture on reverse-colex concatenation of fixed-weight de Bruijn sequences

Let $n,t\geq 2$ and let $w<t$. Let $\mathcal{V}_t(n,w)$ be the universal cycle constructed from the relevant fixed-weight strings, and let $\mathcal{V'}_t(n,w)$ be the sequence obtained by concatenating the aperiodic prefixes of the necklaces in $\mathbf{N}_t(n+1)$ of weight $w$ in reverse colex order. Reverse-colex concatenation conjecture. The universal cycle $\mathcal{V}_t(n,w)$ is equivalent to $\mathcal{V'}_t(n,w)$, and the universal cycle can be generated in $\mathcal{O}(1)$ amortized time per symbol. This conjecture concerns the structural relationship between the paper's universal-cycle construction and reverse-colex necklace concatenation; no resolution is supplied in the given text.