Brandt's weak pancyclicity conjecture

A graph is weakly pancyclic if the set of lengths of its cycles forms an interval. Brandt's conjecture. Every non-bipartite graph on $n$ vertices with more than

$$\frac{n^2}{4}-n+\frac{19}{4}$$

edges is weakly pancyclic. This conjecture proposes a sharp extension of Brandt's stability theorem for dense non-bipartite graphs; the supplied source gives no resolution status.