Origin of the missing torus one-point solution

Explain why the torus one-point modular-covariance solution count for the deformed critical loop model is smaller by an additional solution than the expected count after excluding diagonal fields, including the absence of a nonzero solution for r_1=2 and the presence of only one solution for r_1=3.

Background

For trivial phase, the paper compares its conjectured torus one-point solution count with a previously established count of relevant combinatorial maps. Excluding diagonal fields accounts for one missing solution, but the formula contains an additional unexplained subtraction of two.

This unresolved discrepancy is concrete: the paper reports no nonzero solution when r_1=2 and only one solution when r_1=3. Determining the source of this loss would clarify the modular bootstrap of deformed critical loop models.