The conjecture on tritangent planes to tropical sextic curves

Let $\Gamma$ be a tropical sextic curve of genus $4$ in $\mathbb{R}^3$. Two tritangent planes to $\Gamma$ are equivalent when they determine equivalent tangency divisors on $\Gamma$. Tritangent-plane conjecture. Every tropical sextic curve of genus $4$ in $\mathbb{R}^3$ has exactly $15$ equivalence classes of tritangent planes. The preceding theorem proves the upper bound of $15$, and proves equality when the tropical curve is the tropicalization of a sextic on a smooth quadric in $\mathbb{P}^3$; the conjecture asserts equality without that algebraizability hypothesis.