Employing mathematical and empirical methods to explore the supervisory system and the enforcement of su-pervisory laws inaugurates a novel paradigm for research and knowledge creation.This methodology is marked by its use of digital expressions,data analytics,and the characteristics of repeatability and falsifiability in drawing conclusions,significantly enhancing the caliber of scholarly inquiry within the realm of supervisory jurisprudence.Despite its advantages,the current trend in mathematical and empirical investigations,heavily influenced by the traditional leanings towards qualitative research,exhibits a noticeable bias towards topics encompassing the scrutiny,indictment,and adjudication of official misconduct.Such studies frequently undertake expansive themes with a distinct sectoral focus,while the interpretation and elucidation of data of-ten remain underdeveloped.This scenario reveals that mathematical and empirical research in supervisory law predominantly resides in the"let the numbers speak"phase,characterized by an initial quantitative analysis that predominantly relies on de-scriptive representation.This approach falls short of the critical thinking and logical deduction inherent to mathematical and empirical studies.In the digital age,underscored by the advancements in big data and artificial intelligence,there is a pressing need to evolve from a mere numerical narrative towards a robust mathematical intellect.Achieving this transformation necessi-tates the adoption of a scientific mindset that prioritizes the validation of hypotheses,leverages variable assignment and data an-alytics as instrumental tools,and bases reasoning on mathematical logic.This evolution aims to transition from speculative in-terpretations to mathematical validations,from theoretical assertions to empirical refutations,and from descriptive portrayals to deductions of causality.
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