[Submitted on 29 Sep 2026]
Title:Can an AI Agent Rediscover a Blaschke-Curve Invariant?
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Abstract:We study generalized Blaschke curves as a controlled environment for AI-assisted mathematical rediscovery. For one fixed degree-four Blaschke product, an agent receives numerical coordinates of the six pair-lines determined by each of 80 boundary configurations. The target theorem is withheld from the task instructions. The saved research log reports rejected geometric hypotheses and a homogeneous cubic fitted to polygon sides. Its frozen coefficients predict 480 lines from 80 unseen parameter values, with a recorded RMS scale-free residual of $8.88\times10^{-17}$. Discovery-set diagonals provide an out-of-fit consistency check, not a fully held-out test. A separate one-configuration run reports insufficient evidence for invariance. A post-review deterministic degree-search baseline also recovers the cubic, so the experiment does not establish an advantage over polynomial fitting. We present this single-instance case study as a protocol for separating conjecture, numerical validation, and proof, with explicit limitations concerning agent metadata, prior knowledge, and reproducibility.
Comments: Accepted for poster presentation at the NeurIPS 2026 Workshop on Mathematical Reasoning and AI (MATH-AI). 8 pages, 1 figure. Code and data: this https URL
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2609.38369 [cs.AI]
(or arXiv:2609.38369v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.38369
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Yunus Zeytuncu [view email] [v1] Tue, 29 Sep 2026 18:29:57 UTC (1,722 KB)
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