Verification systems are very important for making sure that computer processes are correct and reliable in many areas, such as hacking, software validation, and data quality checks. This study shows a new system that combines machine learning (ML) methods with discrete mathematical models to make testing more accurate and faster. The suggested system uses ideas from vector measure spaces and orthogonal sequences to describe difficult proof tasks on a solid mathematical base. Adding vectorial convergence qualities to the system lets it improve testing results over and over, which cuts down on the false positives and raises the rate of detection.