  The double-spin-polarization observable $\mathbb{E}$ for
$\vec{\gamma}\vec{p}\to p\pi^0$ has been measured with the CEBAF Large
Acceptance Spectrometer (CLAS) at photon beam energies $E_\gamma$ from 0.367 to
$2.173~\mathrm{GeV}$ (corresponding to center-of-mass energies from 1.240 to
$2.200~\mathrm{GeV}$) for pion center-of-mass angles,
$\cos\theta_{\pi^0}^{c.m.}$, between -0.86 and 0.82. These new CLAS
measurements cover a broader energy range and have smaller uncertainties
compared to previous CBELSA data and provide an important independent check on
systematics. These measurements are compared to predictions as well as new
global fits from The George Washington University, Mainz, and Bonn-Gatchina
groups. Their inclusion in multipole analyses will refine our understanding of
the single-pion production contribution to the Gerasimov-Drell-Hearn sum rule
and improve the determination of resonance properties.
