We study generalized Blaschke curves as a controlled environment for AI‑assisted mathematical rediscovery. For a fixed degree‑four Blaschke product, the agent receives numerical coordinates of the six pair‑lines determined by each of 80 boundary configurations. The target theorem is omitted from the task description. The research log records rejected geometric hypotheses and a homogeneous cubic fitted to polygon sides. Once frozen, the cubic’s coefficients predict the 480 lines arising from 80 unseen parameter sets with a scale‑free RMS residual of $8.88\times10^{-17}$. Diagonals from the discovery set serve as an out‑of‑fit consistency check rather than a fully held‑out test. A separate run on a single configuration fails to provide sufficient evidence for invariance. A deterministic degree‑search baseline later recovers the same cubic, indicating no advantage over ordinary polynomial fitting. We present this single‑instance case study as a protocol to separate conjecture, numerical validation, and formal proof, while explicitly noting limitations regarding agent metadata, prior knowledge, and reproducibility.
Review