Pipe Dream Rectification and Dual RSK Correspondence

We prove Dennin’s conjecture (Conjecture 8.9 of arXiv:2506.21052) that his variant of dual RSK correspondence is symmetric when restricted to biGrassmannian permutations. For a binary matrix $A$, let $A^{†}$ denote its transpose-complement, and let $\mathrm{ins}(A)$ and $\mathrm{rec}(A)$ denote its insertion and recording tableaux. We prove that $\mathrm{ins}(A^{†})=\overline{\mathrm{rec}(A)}$, where the bar denotes the natural complement of the recording tableau. Our proof uses rectification of super pipe dreams and a downward induction on suffixes of $A$.