JULIA SETS AND BIFURCATION LOCI

The paper proves Jh ≠ Sbif ≠ Jf ≠ Jh by reducing set equalities to equalities of Green functions/measures and deriving contradictions via pluripotential and laminar-current arguments (Theorems 1.1 and 2.3) . By contrast, the candidate’s proof hinges on comparing closures in P^2 at the line at infinity L∞. Its key step asserts cl(Jf) ∩ L∞ = {I+, I−}, but Jf is compact in C^2 (as supp(µf)), so its closure in P^2 does not meet L∞ at all, contradicting the claim and invalidating the subsequent “separation at infinity” argument . The paper’s measure-based separations (e.g., Theorem 4.1 and Proposition 4.2 for Jh ≠ Jf; and the extremality argument for Jf ≠ Sbif) are internally consistent and do not rely on behavior at L∞ .