Independence of the intersection tree from the Whitney tower

Let $A_1,\dots,A_m$ be the original maps, let $\mathcal{W}$ be a Whitney tower on them, and let $\tau_n(\mathcal{W})$ be its intersection tree, regarded as an element of the quotient $\mathcal{T}_n(\pi,m)/\mathrm{INT, FR}$. The original maps have regular homotopy classes given by their equivalence classes under regular homotopy. Whitney-tower independence conjecture. The intersection tree

$$\tau_n(\mathcal{W})\in \mathcal{T}_n(\pi,m)/\mathrm{INT, FR}$$

is independent of the choice of the Whitney tower $\mathcal{W}$. In fact, it only depends on the regular homotopy classes of the original maps $A_i$, and should be written as $\tau_n(A_1,\dots,A_m)$. The INT and FR relations account for indeterminacies arising from choices of Whitney-disk interiors and framings; the paper provides evidence for this conjecture by proving a closely related special case, while the full statement is not resolved here.