The unrestricted generic-kernel divisor conjecture

Let $\mathfrak{O}(V^{(i)}_k,V^{(j)}_l)$ be the divisor of the normalized $R$-matrix denominator, and let $\dim_{q^{-1}}\mathop{\mathrm{ext}}^1_{\widetilde{\Pi}}$ denote the graded extension dimension between the generic kernels $K^{(i)}_k$ and $K^{(j)}_l$. Unrestricted divisor–extension conjecture. For any $i,j\in I$ and $k,l\in\mathbb{Z}_{>0}$,

$$\mathfrak{O}(V^{(i)}_k,V^{(j)}_l)=\dim_{q^{-1}}\mathop{\mathrm{ext}}^1_{\widetilde{\Pi}}(K^{(i)}_k,K^{(j)}_l).$$

This generalizes the conditional divisor conjecture by asserting the equality without the inequality $kd_i\ge ld_j$ or the exceptional condition $(\clubsuit)$.