发表机构
University of Michigan-Dearborn（密歇根大学迪尔伯恩分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究以广义Blaschke曲线为环境，测试AI代理能否重新发现数学不变量，通过数值拟合与基线对比，提出区分猜想、验证与证明的协议。
AI 中文摘要
我们将广义Blaschke曲线作为AI辅助数学重新发现的可控环境进行研究。对于一个固定的四次Blaschke乘积，代理接收由80个边界配置中的每一个确定的六对线对的数值坐标。目标定理从任务说明中被隐去。保存的研究日志记录了被拒绝的几何假设以及拟合到多边形边上的齐次三次多项式。其冻结系数从80个未见过的参数值预测出480条线，记录的均方根无标度残差为$8.88\ imes10^{-17}$。发现集的对角线提供了拟合外的一致性检查，而非完全独立的测试。一次单独的单配置运行报告了不变量证据不足。事后审查的确定性次数搜索基线也恢复了该三次多项式，因此该实验并未确立相对于多项式拟合的优势。我们将此单实例案例研究作为区分猜想、数值验证和证明的协议，并明确说明代理元数据、先验知识和可复现性方面的局限性。
英文摘要
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.
CommentsAccepted for poster presentation at the NeurIPS 2026 Workshop on Mathematical Reasoning and AI (MATH-AI). 8 pages, 1 figure. Code and data: https://github.com/yezeytuncu/blaschke-ai-rediscovery
