Not yet reviewed by Pith; the record is open.

One of the most striking manifestations of orderly behavior emerging out of complex interactions in any astrophysical system is the 11-year cycle of sunspots. However, direct sunspot observations and reconstructions of long-term solar activity clearly exhibit amplitude fluctuations beyond the decadal timescale -- which may be termed as supradecadal modulation. Whether this long-term modulation in the Sun's magnetic activity results from nonlinear mechanisms or stochastic perturbations remains controversial and a matter of active debate. Utilizing multi-millennial scale kinematic dynamo simulations based on the Babcock-Leighton paradigm -- in the likely (near-critical) regime of operation of the solar dynamo -- we demonstrate that this supradecadal modulation in solar activity cannot be explained by nonlinear mechanisms alone; stochastic forcing is essential for the manifestation of observed long-term fluctuations in the near-critical dynamo regime. Our findings substantiate some independent observational and theoretical investigations, and provide additional insights into temporal dynamics associated with a plethora of natural phenomena in astronomy and planetary systems arising from weakly nonlinear, non-deterministic processes.