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\section{Discussion and Conclusions} \label{sec:discussion} \section{Nonlinear Combination Frequencies} \label{sec:nonlinear} In addition to the 20 significant independent pulsation modes we identify in Section\,\ref{sec:analysis} Section~\ref{sec:analysis} we see a number of nonlinear combination frequencies that arise at summed and difference frequencies of the independent modes. For example, the peak at 2107.3\,\muhz\ is a linear sum of the two independent pulsations $f_4=940.3$\,\muhz\ and $f_7=1166.2$\,\muhz, within the uncertainties. Combination frequencies are a common feature in the pulsation spectra of variable WDs, which are created by a nonlinear distortion of an underlying linear oscillation signal. Early work by \citet{1992MNRAS.259..529B} attributed these nonlinear distortions to the changing thickness of the convection zone of a DAV, a result of local surface temperature variations from the underlying global stellar oscillations. The convection zone depth is extremely sensitive to temperature ($\propto T^{-90}$, \citealt{2005ApJ...633.1142M}), distorting the observed emergent flux. For the hottest DAVs, the nonlinear response of the flux to a temperature perturbation (i.e., the ``$T^4$'' nonlinearity) may play a role in creating these signals \citep{1995ApJS...96..545B}. Observations of the rate of period change of combination frequencies show that they match identically the rates of their parent modes, proving that these signals are not independently excited pulsations but rather nonlinear distortions \citep{2013ApJ...766...42H}. Thus, these signals provide no additional asteroseismic constraints on the interior structure of the star. However, the amplitude ratios of these combination frequencies to their parent modes can yield insight into the depth of the convection zone, which is responsible for driving the underlying pulsations (e.g., \citealt{2010ApJ...716...84M,2012ApJ...751...91P}). We detail the observed nonlinear combination frequencies in GD\,1212 and identify their likely parent modes in Table\,\ref{tab:freq}. Table~\ref{tab:freq}. Their amplitudes and frequencies were determined in an identical manner to the independent pulsation modes, as discussed in Section\,\ref{sec:analysis}. Section~\ref{sec:analysis}. However, we have used a less stringent test for significance, and include as significant the signals that exceed 4$\sigma$.The We mark these adopted nonlinear combination frequencies as magenta points in our FT of all the data, shown in the top panel of Figure\,\ref{fig:GD1212ft}. Figure~\ref{fig:GD1212ft}. We show a more detailed view of the regions of these combination frequencies in Figure\,\ref{fig:GD1212combos}. Figure~\ref{fig:GD1212combos}. Good evidence that these are in fact combination frequencies comes qualitatively from the region in the FT near 2006\,\muhz\ (bottom panel of Figure\,\ref{fig:GD1212combos}) Figure~\ref{fig:GD1212combos}) as compared to the region near 847\,\muhz\ (middle panel, Figure\,\ref{fig:GD1212ft}). Figure~\ref{fig:GD1212ft}). There appear two combination frequencies, 2006.6\,\muhz\ and 2011.5\,\muhz, which are combination of $f_1+f_7$ and $f_5+f_7$, respectively. The power for the $f_5+f_7$ combination frequency is nearly nonexistent in our final 9.0 days of data, exactly as the power for $f_5$ near 847.2\,\muhz\ is diminished in our final 9.0 days of data. Unfortunately, the underlying frequency variability of the independent parent modes extends to these combination frequencies, broadening their power in an FT, so these nonlinearities do not provide much assistance in refining the periods of the parent modes. But the eight significant low-frequency difference frequencies, ranging from $19.2-170.0$\,\muhz\ ($1.6-14.5$ hr), are the longest-period signals detected in a pulsating WD, accessible only because of the exceptionally long and uninterrupted observations provided by {\em Kepler}. {\it Facilities:} Kepler We preliminarily identify the variability at $f_{21}=371.1$\,s and $f_{19}=369.8$\,s as independent pulsation modes, but they arise at substantially shorter periods, far isolated from the other independent pulsations, which are all longer than 828.2\,s. The signals $f_{21}$ and $f_{19}$ may instead be more complicated nonlinear combination frequencies. For example, $f_{21}$ may be the sum $2f_1+f_2$. However, no obvious frequency combination can produce the higher-amplitude $f_{19}$. These signals may also be new instrumental artifacts in {\em K2}.