Upper bound conjecture for zeros of Wronskians of disconjugate equations

Let

$$y^{(n)}+p_1(x)y^{(n-1)}+\ldots+p_n(x)y=0$$

be a linear ordinary homogeneous differential equation of order $n$ with real-valued continuous coefficients, disconjugate on an interval $I$. For a positive integer $1\leq k\leq n-1$, let $(y_1(x),y_2(x),\dots,y_k(x))$ be any $k$-tuple of linearly independent solutions. Wronskian zero bound conjecture. The number of real zeros on $I$, counting multiplicities, of

$$\det(W(y_1(x),y_2(x),\dots,y_k(x)))$$

does not exceed $k(n-k)$. This conjecture concerns a proposed uniform bound for consecutive Wronskians in disconjugate linear differential equations; the case $k=2$, $n=4$ has been settled, while the general statement remains open.