Generic equality of the true and counting synthesis filter lengths

Let $C$ analysis channels be arranged in a $D$-fold subsampled FIR analysis bank $h_ig_{i=1}^{C}$ with analysis filter length $m_h>D$. Let $m_v^{\ast}(C,D,m_h)$ denote the true minimal synthesis filter length at which perfect reconstruction becomes feasible, and let $m_v^{{\textsc C}}(C,D,m_h)$ denote the counting length.

Counting-length conjecture. Generically, a length-$m_v$ FIR synthesis bank achieving perfect reconstruction exists if and only if

$$m_v\geq m_v^{{\textsc C}}(C,D,m_h).$$

The conjecture asserts that the counting length is both necessary and sufficient, so that $m_v^{\ast}(C,D,m_h)=m_v^{{\textsc C}}(C,D,m_h)$. The paper presents simulation evidence for this claim; the surrounding necessary and sufficient bounds alone do not establish the equality.