We present the identification of very low frequency g modes, in the asymptotic regime, and two important parameters: the core rotation rate and the asymptotic equidistant period spacing of these g modes. The GOLF instrument on the SOHO space observatory has provided two decades of full disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult, due to solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently, searching for possible collective frequency modulations produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. For oscillatory periods in the range between 9 and nearly 48 hours, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. P0, the g-mode period equidistance parameter, is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non synodic reference with a very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3:8 ± 0:1 faster than the rotation of the radiative envelope.