Rivin's bounded multiplicity conjecture for simple length spectra

Let $M$ be a hyperbolic surface. The multiplicity of a length in the simple length spectrum is the number of distinct simple closed geodesics on $M$ having that length.

Rivin's conjecture. The multiplicity in the simple length spectrum is bounded above by a constant depending only on the topology of the surface.

This predicts a uniform topological bound despite the variation of hyperbolic metrics. The source attributes the conjecture to Rivin but gives no resolution status.