On planar holomorphic systems

The core classification counts for ż=f (degrees 2,3,4 → 3,9,22) and for Möbius systems (9 classes) in the candidate match the paper’s theorems (Theorems 16, 21, 28, 39). For ż=1/f, the candidate’s counts 3,4,11 agree with the explicit enumerations in Theorems 33–35 (3 for quadratic, 4 for cubic, 11 for quartic), while the paper’s introductory summary incorrectly states 3,11,8; the internal inconsistency is in the paper’s summary, not its detailed theorems. However, the candidate makes technical errors: it claims n−2 pairs of saddles at infinity for ż=f (the paper states n−1 pairs), and it gives the wrong number of elliptic sectors at multiple zeros (the paper states 2n−2). Hence both contain issues: the paper’s summary is inaccurate for ż=1/f, and the model’s supporting arguments have mistakes even though its main counts align with the paper’s theorems. Key citations: Theorem 16 (quadratic: 3 portraits), Theorem 21 (cubic: 9; 6 if nodes/foci not distinguished), Theorem 28 (quartic: 29 if distinguishing; 22 otherwise), Theorem 33 (1/f, deg 2: 3), Theorem 34 (1/f, deg 3: 4), Theorem 35 (1/f, deg 4: 11), Theorem 39 (Möbius: 9), Theorem 12 (first integral H=Im G), preliminaries on infinity (n−1 saddle pairs) and local multiplicity/sector count.