Perfect local-cohomology pairing for finite arc algebras

Let $J^N$ be the finite arc algebra and let $\mathfrak{i}_k$ and $\mathfrak{j}_k$ be the support ideals generated respectively by the initial and terminal arc coefficients as defined in the source. Finite arc-algebra duality conjecture. There is a perfect pairing

$$H^i_{\mathfrak{i}_k}(J^N)\otimes H^{-i+8N+16}_{\mathfrak{j}_k}(J^N)\to\mathbb{C}.$$

Such a pairing would provide a finite-level duality for local cohomology supported on the two complementary arc-coordinate subschemes.