The phylogenetic invariants conjecture for binary trees

Let $\tau$ be a binary tree on binary random variables, and let $I_f$ be the ideal of phylogenetic invariants of its general Markov model. Each edge of $\tau$ induces a split of the leaves, and flattening the $2 \times \cdots \times 2$ table $(p_{\sigma_1 \cdots \sigma_n})$ along a split produces a two-dimensional matrix. The phylogenetic invariants conjecture. The ideal $I_f$ is generated by the $3 \times 3$ determinants of all such flattenings. The set-theoretic version was announced as proved by Allman and Rhodes, which identifies the radical of the determinantal ideal with $I_f$; the asserted ideal-theoretic generation remains the stronger statement.