Schmutz-Schaller's multiplicity conjecture for the simple length spectrum

A once-punctured torus is a hyperbolic surface whose simple closed geodesics have a length spectrum, with multiplicity counting how many distinct simple closed geodesics have a given length. Schmutz-Schaller's conjecture. The multiplicity of the simple length spectrum is bounded above by $6$ for a once-punctured torus. The existence of an upper bound for this multiplicity was open in general for surfaces of fixed signature; this conjecture gives the proposed bound in the once-punctured-torus case.