Angular Momentum Co-Resonance: A Unified Mathematical Theory from Conservation Laws to Resonance

Traditional resonance theories take the maximum energy transfer under frequency matching as the core criterion, which is insufficient for physical scenarios dominated by angular momentum, such as rotating systems, quantum transitions and gravitational wave detection. Based on the law of conservation of angular momentum, this paper establishes a unified mathematical framework for angular momentum co-resonance. We prove that the essence of resonance lies in the frequency matching between the rate of change of angular momentum of the driving source and the intrinsic angular momentum modes of the system. By introducing the angular momentum response function and angular momentum impedance, the general equations of angular momentum co-resonance are derived. Comparative analysis shows that angular momentum co-resonance is mathematically equivalent to conventional energy resonance in conservative linear systems, while it yields new observable predictions for dissipative and nonlinear systems. Combined with the Unified Vacuum Medium Model (UVMM), this work predicts the circular polarization degree of primordial gravitational waves and pulsar timing offset near the Sun per 30 minutes, as well as the amplitude of CMB TB odd-parity spectrum . All predictions contain no free adjustable parameters and are consistent with existing astronomical observations. Clear falsification thresholds are set for future experimental tests. This study provides a new theoretical reference for space gravitational wave detection, radio astronomy and CMB observations.