On the separatrix graph of a rational vector field on the Riemann sphere

The paper proves the characterization via rectified zones, gluing, and uniformization on the sphere, while the model derives the same admissibility conditions using the quadratic differential q=(dz/R)^2 and cites Jenkins–Strebel-style existence for the converse. The model’s local and global counts match the paper’s conditions (a)–(i), with only a minor looseness (it states r(b)≤2s−2 where the paper has equality r(b)=2s−2). The paper’s construction is complete, and the model’s approach is mathematically sound though it compresses the existence step to well-known results in the quadratic-differential literature.