The Compton double-polarization observable $Sigma_{2z}$ has been measured for the first time in the $Delta(1232)$ resonance region using a circularly polarized photon beam incident on a longitudinally polarized target at the Mainz Microtron. This paper reports these results, together with the model-dependent extraction of four proton spin polarizabilities from fits to additional asymmetry data using dispersion relation and chiral perturbation theory calculations, with the former resulting in: $gamma_{E1E1} = -3.18 pm 0.52$, $gamma_{M1M1} = 2.98 pm 0.43$, $gamma_{E1M2} = -0.44 pm 0.67$ and $gamma_{M1E2} = 1.58 pm 0.43$, in units of $10^{-4}~mathrm{fm}^{4}$.
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