Spectral index evolution of the limb-brightened jet in 3C 84

Relativistic jets launched by active galactic nuclei are fundamental for understanding the physics of accreting supermassive black holes and their immediate environment, yet the mechanisms driving jet launching remain uncertain. In this study, we investigate the sub-parsec jet of 3C 84 using multi-epoch, multi-frequency, very long baseline interferometry (VLBI) observations with the European VLBI Network and the Very Long Baseline Array at 22 and 43 GHz. We analyse the evolution of the spectral index gradient in the core region to relate the observed structure to physical interpretations and to discriminate between competing jet launching models. Furthermore, we examine the impact of the ambient medium and magnetic field configuration on jet morphology and dynamics over time, and explore their connection to a coinciding $γ$-ray flare. Our spectral analysis reveals significant changes across three epochs, indicating dynamic activity between filamentary structures on sub-parsec scales, evolving magnetic fields, and a complex interaction with the surrounding medium, all of which shape the innermost jet and may influence its high-energy emission.