Coincidence threshold of even-dimensional Chebyshev hypersurfaces

Let ${\mathcal C}(n,d)$ be the Chebyshev hypersurface of degree $d$ in $\mathbb{P}^n$, where $n=2n_1$ is even. Write $ct(D)$ for the coincidence threshold of a hypersurface $D$. Coincidence-threshold conjecture.

If $n=2n_1$ is even, then

$$ct({\mathcal C}(n,d))=(n_1+1)d-n-2.$$

Thus the bounds given earlier for Chebyshev hypersurfaces are best possible in this case.

This claim concerns the exact coincidence threshold for even-dimensional Chebyshev hypersurfaces; the supplied text presents it as a conjecture and gives no resolution evidence.