Spectral Evolution of Solar Mean Magnetic Field Rotation Periods: A 50-Year Analysis of Differential Band Dominance, Carrington Episodicity, and the κ_URC Resonance in WSO Data

Analysis of Wilcox Solar Observatory (WSO) Solar Mean Magnetic Field (SMMF) data spanning 1975–2024 (solar cycles 21–25). Reports three findings: (1) a coherent 50-year exchange of dominance between fast (~26.875 day) and slow (~27.166 day) solar rotation bands; (2) episodic rather than stable Carrington period amplitude in the SMMF spectrum; (3) an empirical relationship between the power-weighted spectral centroid and the product of fundamental constants π × φ × α (the κ_URC resonance, 26.959 days). Data source: WSO public archive, Stanford University.