Trotman's tubular-neighborhood conjecture for b-regular stratified spaces

Let $(A,\Sigma)$ be a differentiable stratified space $b$-regularly embedded by $p$ into $\mathbb R^n$: for strata $Y<X$, whenever sequences in $X$ and $Y$ converge to a point of $Y$, the limiting direction from the points of $X$ to the points of $Y$ lies in the limiting tangent space to $X$. For every stratum $X\in\Sigma$ and point $x\in X$, there should exist a neighborhood $U$ of $x$ and a tubular neighborhood $(L,\mathcal L)$ of $X_{|U}$ in $(U,\Sigma_{|U})$ such that the restriction $p_{|L}$ is an embedding of $(L,\mathcal L)$. Trotman's conjecture. Every differentiable stratified space satisfying this $b$-regular embedding condition has such a locally embedded tubular neighborhood around each stratum. The conjecture is D. Trotman's 1993 adaptation of Whitney's conjecture to differentiable stratified spaces; the supplied text gives no resolution status.