Cat Factoring: A Structured Mathematical Thinking Framework for Quadratic Factorization

Cat Factoring is a structured mathematical thinking framework for quadratic factorization. Rather than introducing a new algebraic identity, it reorganizes the factorization process into a guided symbolic reasoning structure through a Slot-Check methodology. This approach reduces cognitive load, narrows the effective search pathway, and transforms trial-and-error into a systematic verification process. This work presents the theoretical foundation (CF1) of the Cat Factoring framework and establishes it as a formal educational and symbolic reasoning model. Future work includes computational formalization, interactive educational tools, and empirical validation.