Scalarity conjecture for the root-of-unity knot invariant

Let $q=\omega$ be a root of unity of order $N\geq 1$, let $H_{c,t}$ be the $4N$-dimensional Nichols f-algebra with scaling automorphism $\phi_t x_i=t_i x_i$, and let $R_{c,t}$ be the associated left $R$-matrix. For a knot $K$, write $J_{R_{c,t}}(K)\in\operatorname{End}(H_{c,t})$ for the resulting knot invariant, and let $\Lambda_{\omega,K}(t_1,t_2)$ be its $(1,1)$-entry with respect to the alternating-word basis. Scalarity conjecture. For every knot $K$, we have

$$J_{R_{c,t}}(K)=\Lambda_{\omega,K}(t_1,t_2)\operatorname{id}_{H_{c,t}}.$$

This asserts that the full endomorphism-valued invariant is determined by its $(1,1)$-entry, strengthening the associated scalar polynomial invariant. The supplied text gives no evidence that the claim has been proved or refuted.