Füredi–Maleki structural conjecture for minimizing triangular edges

Let $m>n^2/4$ and let $G$ be an $n$-vertex graph with $m$ edges that minimizes the number of triangular edges. For integers $a,b,c$, let $G(a,b,c)$ be the graph consisting of a clique of size $a$ and independent sets of sizes $b$ and $c$, with all edges between the set of size $b$ and the other two parts. Füredi–Maleki's conjecture. There exist integers $a,b,c$ such that $G$ is isomorphic to a subgraph of $G(a,b,c)$. This conjecture concerns the structural form of extremal graphs for minimizing triangular edges above the Turán bipartite threshold; the source gives no resolution status.