The compact framed conical approximation conjecture

Let $(\bI^n,f)$ be a compact framed conical stratification, where $\bI^n=[-1,1]^n$. A compact manifold $n$-diagram is a tame stratification of $\bI^n$ that is tame compact framed conical.

Tame diagrams approximate all diagrams. Every compact framed conical stratification $(\bI^n,f)$ has an arbitrarily close approximation by a compact manifold $n$-diagram.

This conjecture proposes that compact framed conical stratifications can be approximated arbitrarily closely by the paper's combinatorially controlled tame objects.