Anomalous Spin Precession Frequency Analysis in the Muon $g-2$ Experiment at Fermilab

The Muon $g-2$ experiment at Fermilab aims to measure the muon anomalous magnetic moment with an unprecedented precision of 140 parts per billion (ppb). Data collection concluded in June 2023, and analysis of the largest dataset (2021-2023) is underway. Previous publications based on data from 2018-2020 established the experimental foundation. This document provides an overview of the measurement of the muon anomalous spin precession frequency ($ω_a$) and the associated systematic corrections. The precision of these results directly tests the Standard Model's completeness, making the experiment a cornerstone in the field of particle physics.