SYNTAGMA-C: Automating Mathematical Discovery Complete Solution to FrontierMath Tier 4 Research Problem

This paper presents the first complete autonomous solution by an AI system of an unpublished research-level mathematics problem. SYNTAGMA-C successfully solved a FrontierMath Tier 4 problem concerning the continuous extension of linear recurrences to p-adic integers. The system determined the statement is false and provided a verified counterexample at p=11, along with a complete 6-step proof. This achievement demonstrates that large language models can now perform authentic mathematical research without training data, external tools, or human intervention. The solution methodology, proof verification, and implications for automated mathematical discovery are detailed herein.