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The strong interaction is not well understood at low energy, or for interactions with low momentum transfer $Q^2$, but one of the clearest insights we have comes from Chiral Perturbation Theory ($χ$PT). This effective treatment gives testable predictions for the nucleonic generalized polarizabilities -- fundamental quantities describing the nucleon's response to an external field. We have measured the proton's generalized spin polarizabilities in the region where $χ$PT is expected to be valid. Our results include the first ever data for the transverse-longitudinal spin polarizability $δ_{LT}$, and also extend the coverage of the polarizability $\bar{d_2}$ to very low $Q^2$ for the first time. These results were extracted from moments of the structure function $g_2$, a quantity which characterizes the internal spin structure of the proton. Our experiment ran at Jefferson Lab using a polarized electron beam and a polarized solid ammonia (NH$_3$) target. The $δ_{LT}$ polarizability has remained a challenging quantity for $χ$PT to reproduce, despite its reduced sensitivity to higher resonance contributions; recent competing calculations still disagree with each other and also diverge from the measured neutron data at very low $Q^2$. Our proton results provide discriminating power between existing calculations, and will help provide a better understanding of this strong QCD regime.