Musiker's positivity conjecture for super lambda-lengths

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Consider the once-punctured torus with the spin structure induced by the cyclic orientation of the two triangles in the fundamental domain, clockwise on one triangle and counter-clockwise on the other. Let the associated decorated super-Teichmüller space have super lambda-lengths assigned to arcs. Musiker's positivity conjecture. The formula for the super lambda-length of every arc can be expressed using only positive coefficients. The conjecture concerns positivity in the Laurent-polynomial formulas arising from the super Markov setting and remains open in the source.

References

Primary source

Léa Bittmann, Perrine Jouteur, Ezgi Kantarcı Oğuz, Melody Molander and Emine Yıldırım, “A mirror deformation of Markov numbers”, arXiv:2602.14802 (2026).

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