The lemon bipartite-space conjecture for almost Finsler manifolds

Let $(M,S,F^{\pm})$ be a bipartite space, where $S$ is the slit and $F^+$ is its positive partial Finsler function. The lemon bipartite-space conjecture. A bipartite space of the form $(M,S,F^+)$ is an almost Finsler manifold. This concerns when the positive, or lemon, indicatrix defines an almost Finsler structure; the supplied text gives no resolution or further conditions.