AI 服務暫時不可用，以下為來源正文，待恢復後補全翻譯。
[Submitted on 29 Sep 2026] Title:Can an AI Agent Rediscover a Blaschke-Curve Invariant? View a PDF of the paper titled Can an AI Agent Rediscover a Blaschke-Curve Invariant?, by Yunus E. Zeytuncu View PDF HTML (experimental) 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) Full-text links: Access Paper: View a PDF of the paper titled Can an AI Agent Rediscover a Blaschke-Curve Invariant?, by Yunus E. Zeytuncu View PDF HTML (experimental) TeX Source view license Current browse context: cs.AI new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)