Super Markoff-number conjecture for the once-punctured torus

Begin with an oriented triangulation of the once-punctured torus described in the source, and retain $e$ as a formal variable rather than setting it equal to $1$. Iterated flips in all three directions produce all possible arcs in the once-punctured torus. Super Markoff-number conjecture. The super $\lambda$-lengths of these arcs are super analogues of the Markoff numbers and have combinatorial interpretations via double dimer covers of the snake graphs appearing in Section 7 of the cited work, with appropriately specialized $\mu$-invariants. This is proposed as a natural extension of the classical Markoff-number and dimer-cover picture; the source supplies no proof, so its status is open.