  Cosmogenic isotopes provide the only quantitative proxy for analyzing the
long-term solar variability over a centennial timescale. While essential
progress has been achieved in both measurements and modeling of the cosmogenic
proxy, uncertainties still remain in the determination of the geomagnetic
dipole moment evolution. Here we improve the reconstruction of solar activity
over the past nine millennia using a multi-proxy approach. We used records of
the 14C and 10Be cosmogenic isotopes, current numerical models of the isotope
production and transport in Earth's atmosphere, and available geomagnetic field
reconstructions, including a new reconstruction relying on an updated
archeo-/paleointensity database. The obtained series were analyzed using the
singular spectrum analysis (SSA) method to study the millennial-scale trends. A
new reconstruction of the geomagnetic dipole field moment, GMAG.9k, is built
for the last nine millennia. New reconstructions of solar activity covering the
last nine millennia, quantified in sunspot numbers, are presented and analyzed.
A conservative list of grand minima and maxima is provided. The primary
components of the reconstructed solar activity, as determined using the SSA
method, are different for the series based on 14C and 10Be. These primary
components can only be ascribed to long-term changes in the terrestrial system
and not to the Sun. They have been removed from the reconstructed series. In
contrast, the secondary SSA components of the reconstructed solar activity are
found to be dominated by a common ~2400-yr quasi-periodicity, the so-called
Hallstatt cycle, in both the 14C and 10Be based series. This Hallstatt cycle
thus appears to be related to solar activity. Finally, we show that the grand
minima and maxima occurred intermittently over the studied period, with
clustering near highs and lows of the Hallstatt cycle, respectively.
