Distinctness conjecture for Chebyshev knot parametrizations

Let $T_n$ denote the degree-$n$ Chebyshev polynomial of the first kind. Let $i,j$ be relatively prime positive integers, and let $k,\ell$ belong to the semigroup denoted by $\ll i,j\gg$ in the source. Distinctness conjecture. If $k\ne\ell$, then

$$(T_i,T_j,T_k)\quad\text{and}\quad(T_i,T_j,T_{\ell})$$

define distinct knots. This is one of the conjectures suggested by the observed patterns for knots arising from reduced triples; the supplied text gives no resolution status.