Algebraic Zero Curves of Homogeneous Plurisubharmonic Polynomials

Let p be a nonzero homogeneous plurisubharmonic polynomial on C^2. We prove that every irreducible affine algebraic curve avoiding the origin on which p vanishes is exactly a nonzero level of a homogeneous holomorphic polynomial of degree at most degree(p). No smoothness or rationality assumption is needed. A finite-pole rigidity lemma on the compact normalization eliminates polar leading terms by Levi positivity. Constancy along complex dilations then yields a holomorphic level by polarization and a binary-form irreducibility argument. This answers the irreducible-curve interpretation of Stensones's 2010 AIM question, recorded as AIM-SEVERAL_COMPLEX_VARIABLES-0028 in ulamai/UnsolvedMath v1.6.0. If reducible curves are allowed, a degree-eight counterexample is given even with no pluriharmonic terms. The two interpretations are distinguished explicitly; the adjacent Newton-diagram problem is not covered. The release includes a five-page English manuscript, standalone LaTeX source, a reproducible Sympy checker with 39 exact regression checks, and a verification report. The proof is the written all-degree argument, not an extrapolation from finite tests. AI-assisted, self-audited and unrefereed. No independent review or proof-assistant formalization is claimed. Novelty and absolute priority remain undetermined after a bounded primary-source comparison.