Perfect-pairing conjecture for logarithmic K-theory

Let $X$ be as above, let $d=\dim(X)$, and take integers $m,m',r,r'$ with $m,m'\geq 0$, $m+m'=2d$, and $m-2r=m'-2r'\geq 0$. The construction in the source gives a pairing

$$K(X,m,r)\times K(X,m',r')\longrightarrow\mathbb{Q}.$$

Perfect-pairing conjecture. This pairing is perfect, and both vector spaces are finite-dimensional over $\mathbb{Q}$. This is proposed as a logarithmic intersection-theoretic counterpart of Poincaré duality; no resolution is stated.