SMMAN Studies of AGN Variability. I. Long-term Spectral Evolution and a Candidate $\sim1000$-day Quasi-periodic Modulation in 4C+72.28
The SMMAN project has carried out nine years of radio flux monitoring in the C and K bands of the blazar 4C+72.28. The two bands show markedly different secular evolution, with a substantially stronger K-band decline producing a gradual decrease in the C-K spectral index. After accounting for this secular evolution, multiple timing diagnostics reveal a candidate quasi-periodic modulation with a characteristic timescale of $\sim1000$ d, most clearly in the C band. The C-band GLSP peak reaches a local significance of $3.29σ$, while its global significance remains modest at $\sim2σ$ and the monitoring baseline covers only about three cycles. Independent and joint MCMC fits support a phenomenological decomposition for both bands into a long-term linear trend and a recurrent component. Under the shared-period assumption, the joint fit returns a characteristic timescale of approximately 1027 d and a similar fractional recurrent amplitudes of $\simeq5.45\%$. Information-criterion comparisons favor the combined linear-plus-sinusoidal model in both bands. Cross-correlation analysis shows a nominal K-leading offset in the original light curves but a centroid consistent with zero lag after detrending, although the lag distributions overlap substantially. These results are consistent with a common recurrent modulation superposed on slower frequency-dependent jet evolution. Geometrical Doppler-factor modulation provides one plausible interpretation, although intrinsic and opacity-related processes cannot be excluded.