On the weak synchronization of a nonlinear solar dynamo oscillator by coherent planetary timing

The solar cycle is commonly interpreted as an internally generated magnetic oscillation, yet its phase stability and long-term amplitude modulation remain difficult to explain through autonomous dynamo physics alone. We test the narrower hypothesis that the solar dynamo behaves as a self-excited nonlinear oscillator whose phase and envelope may be weakly modulated by coherent astronomical timing. Using historical sunspot numbers, terrestrial length-of-day records, and ephemeris-based planetary descriptors, we identify shared long-period pseudo-cycles across solar, geophysical, and astronomical observables. Singular Spectrum Analysis is used only as a non-parametric decomposition method. We then drive a reduced nonlinear α -- Ω oscillator with prescribed planetary timing signals. Solar barycentric angular momentum is treated as a mechanically defined ephemeris descriptor, whereas summed planetary right ascension is retained solely as an empirical geometrical phase proxy. We also introduce the physical planetary quadrupolar tidal tensor and use its equatorial off-diagonal component, 2T xy, as an independent timing descriptor. Forcing by normalized 2T xy yields synchronization comparable to, and slightly better than, right ascension: r=0.660 and RMSE* z =0.824, versus r=0.655 and RMSE* z =0.831. Planetary forcing is not proposed to power or replace the internal dynamo, but only to provide weak timing. A possible relay involves planetary tides, tachocline magneto-Rossby dynamics, and nonlinear dynamo response. These results do not establish a complete coupling mechanism, but support the possibility that the solar cycle is susceptible to weak astronomical synchronization.