Pinching cones for positive isotropic curvature in dimensions seven and eight

We construct and prove the transversal invariance of two families of pinching cones for the Hamilton ODE $\frac{\mathrm{d}}{\mathrm{d}t}R=Q(R)$ in dimensions $n=7,8$, thereby extending the pinching estimate established by Brendle for $n\geq 12$ and by Chen for $9\leq n\leq 11$. In dimension $n=8$, t