Here we go through and compute the tropical data associated to a stable log map \((C,f,p_1)\) with target the toric \(\mathbb P^1\) where \(f:C\to \mathbb P^1\) is degree \(2\).
- contact orders \(u_p\) and \(u_q\) are fixed by the type
- \(V_\eta\) and \(\ell_q\) are allowed to vary, but are fixed by the type if \(Q\) is the basic monoid.
Even given this, the possible contact orders are in some way constrained by the degree via the balancing condition.