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[2602.18918] Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)
Summary
This article presents a case study on the use of ChatGPT-5.2 for resolving a mathematical conjecture, highlighting the role of consumer LLMs in research workflows.
Why It Matters
As large language models (LLMs) become integral in scientific research, understanding their effectiveness and limitations in mathematical proofs is crucial. This study provides early evidence of LLMs' potential in enhancing research productivity while emphasizing the necessity of human oversight.
Key Takeaways
- LLMs can assist in high-level proof search but require human validation for accuracy.
- The study documents an iterative process of generating and refining mathematical proofs using ChatGPT-5.2.
- Insights from this research can inform the design of AI-assisted theorem proving systems.
Computer Science > Artificial Intelligence arXiv:2602.18918 (cs) [Submitted on 21 Feb 2026] Title:Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking) Authors:Brecht Verbeken, Brando Vagenende, Marie-Anne Guerry, Andres Algaba, Vincent Ginis View a PDF of the paper titled Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking), by Brecht Verbeken and 4 other authors View PDF HTML (experimental) Abstract:Large Language Models (LLMs) are increasingly used as scientific copilots, but evidence on their role in research-level mathematics remains limited, especially for workflows accessible to individual researchers. We present early evidence for vibe-proving with a consumer subscription LLM through an auditable case study that resolves Conjecture 20 of Ran and Teng (2024) on the exact nonreal spectral region of a 4-cycle row-stochastic nonnegative matrix family. We analyze seven shareable ChatGPT-5.2 (Thinking) threads and four versioned proof drafts, documenting an iterative pipeline of generate, referee, and repair. The model is most useful for high-level proof search, while human experts remain essential for correctness-critical closure. The final theorem provides necessary and sufficient region conditions and explicit boundary attainment constructions. Beyond the mathematical result, we contribute a process-level characterization...
