Schmutz Schaller's multiplicity-six conjecture for once-punctured tori

Let $M$ be a once-punctured hyperbolic torus, and let the multiplicity of a length in its simple length spectrum mean the number of distinct simple closed geodesics having that length.

Schmutz Schaller's conjecture. The multiplicity is bounded above by $6$.

This is a special case of the general bounded-multiplicity problem and is described as a geometric generalization of the Markov uniqueness conjecture. The source gives no resolution status.