Musiker's positivity conjecture for super lambda-lengths

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.

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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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