The apple bipartite-space conjecture for almost Finsler manifolds

Let $(M,S,F^{\pm})$ be a bipartite space, where $S$ is the slit, $S_x=\ker(s_x)$ is its fibre at $x\in M$, and $F^-$ is the negative partial Finsler function. The apple bipartite-space conjecture. A bipartite space of the form $(M,S,F^-)$ is an almost Finsler manifold if and only if, for all $x\in M$, the slit satisfies

$$\dim S_x\in\{0,\dim M,\dim M-1\}.$$

This gives a necessary and sufficient fibrewise dimension condition for the negative, or apple, indicatrix to define an almost Finsler manifold; the supplied text gives no resolution or further context.