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For perfect wave trapping in the core, purely dipole modes only exist in the envelope, with part of their energy leaking into the core as running magneto-gravity waves. If some wave energy does escape the core, it may leave a signature in the form of mixed magneto-gravity acoustic modes, {\bf or by producing magnetic mode splitting}, which could be used to constrain the internal magnetic field geometry.  In principle, it is possible that another symmetry-breaking mechanism within the core could suppress dipole mode amplitudes. The only other plausible candidate is rapid core rotation. In order for rotation to strongly modify the incoming waves such that they will be trapped in the core, the core must rotate at a frequency comparable to $\nu_{\rm max}$, roughly two orders of magnitude faster than the values commonly observed {\bf measured}  in red giant cores \cite{Beck_2011,Mosser_2012,deheuvels_2014}. The suppressed pulsator KIC 8561221 KIC8561221  \cite{Garcia_2014} does not exhibit rapid envelope rotation and disfavors the rotation scenario. A magnetic field of amplitude $B > 10^4 \, {\rm G}$ (see Figure \ref{fig:Bc}) could be present in the core of a red giant if it retains a fossil field from star formation, or if a convective core dynamo was at work during the main sequence (supplementary online text). These strong fields may reside within the inner core with little external manifestation apart from the suppressed visibility of the dipole modes. However, fields of similar amplitude have been discussed in order to explain the suppression of thermohaline mixing in a small fraction of red giant stars, as inferred from the observations of their surface abundances \cite{Charbonnel_2007}. The {\bf inferred core field strength of $B_r \gtrsim 1.5 \times 10^7 \, {\rm G}$ in KIC8561221} shows very strong magnetic fields ($B \gg 10^6 \, {\rm G}$) can exist within the radiative cores of early RGB stars. Since these fields are likely inherited from previous stages of stellar evolution, slightly weaker ($B \gg 10^5 \,{\rm G})$ fields likely exist within the cores of some main sequence stars. 
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