Can an AI Agent Rediscover a Blaschke-Curve Invariant?

We propose generalized Blaschke curves as a controlled testbed for AI-assisted mathematical discovery. A degree-four finite Blaschke product maps each parameter $\lambda$ on the unit circle to four roots. The six lines determined by pairs of roots are tangent to a parameter-independent class-three algebraic curve. We withhold this fact from an agent and provide only normalized line coordinates from 80 parameter values. The agent rejects simpler fixed-point and conic hypotheses, discovers a homogeneous cubic in the dual projective plane, extends it from polygon sides to diagonals, and freezes its equation before evaluation. When evaluated on 480 lines from 80 unseen parameter values, the frozen cubic attains an RMS scale-free residual of $8.88\times10^{-17}$. In a data-scarcity ablation with one parameter value, an independent agent correctly diagnoses non-identifiability and does not recover the cubic. The experiment illustrates a compact protocol for separating observation, conjecture, held-out validation, and proof in automated mathematical research.