  No state of matter can be defined categorically by what it is not; yet spin
liquids are often conjectured to exist based on the nonexistence of magnetic
order as $T \to 0$. An emerging concept designed to circumvent this ambiguity
is to categorically identify each spin liquid type by using its spectrum of
spontaneous spin noise. Here we introduce such a spectroscopy to spin liquid
studies by considering Ca$_{10}$Cr$_7$O$_{28}$. This is a spin liquid, but
whether classical or quantum and in which specific state, are unknown. By
enhancing the flux-noise spectrometry techniques introduced for magnetic
monopole noise studies, here we measure the time and temperature dependence of
spontaneous flux $\varPhi(t,T)$ and thus magnetization $M(t,T)$ of
Ca$_{10}$Cr$_7$O$_{28}$ samples. The resulting power spectral density of
magnetization noise $S_M(\omega,T)$ along with its correlation function
$C_M(t,T)$, reveal intense spin fluctuations spanning frequencies $0.1\
\mathrm{Hz} \leq \omega/2\pi \leq 50\ \mathrm{kHz}$, and that
$S_M(\omega,T)\propto \omega^{-\alpha(T)}$ with $0.84 < \alpha(T) < 1.04$.
Predictions for quantum spin liquids yield a frequency-independent spin-noise
spectrum, clearly inconsistent with this phenomenology However, when compared
to Monte Carlo simulations for a 2D spiral spin liquid state that are
accurately parameterized to describe Ca$_{10}$Cr$_7$O$_{28}$, comprehensive
quantitative correspondence with the data including $S_M(\omega,T)$, $C_M(t,T)$
and magnetization variance $\sigma_M^2(T)$ fingerprint the state of
Ca$_{10}$Cr$_7$O$_{28}$ as a spiral spin liquid.
