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The spin-structure functions $g_1$ and $g_2$, and the spin-dependent partialcross-section $\sigma_\mathrm{TT}$ have been extracted from the polarizedcross-sections differences, $\Delta\sigma_{\parallel}\hspace{-0.06cm}\left(\nu,Q^{2}\right)$ and $\Delta\sigma_{\perp}\hspace{-0.06cm}\left(\nu,Q^{2}\right)$ measured for the$\vec{^\textrm{3}\textrm{He}}(\vec{\textrm{e}},\textrm{e}')\textrm{X}$reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons withenergies from 1.147 to 4.404 GeV were scattered at angles of 6$^{\circ}$ and9$^{\circ}$ from a longitudinally or transversely polarized $^{3}$He target.The data cover the kinematic regions of the quasi-elastic, resonance productionand beyond. From the extracted spin-structure functions, the first moments$\overline{\Gamma_1}\hspace{-0.06cm}\left(Q^{2}\right)$,$\Gamma_2\hspace{-0.06cm}\left(Q^{2}\right)$ and$I_{\mathrm{TT}}\hspace{-0.06cm}\left(Q^{2}\right)$ are evaluated with highprecision for the neutron in the $Q^2$ range from 0.035 to 0.24~GeV$^{2}$. Thecomparison of the data and the chiral effective field theory predictionsreveals the importance of proper treatment of the $\Delta$ degree of freedomfor spin observables.

Measurement of the 3He Spin-Structure Functions and of Neutron (3He) Spin-Dependent Sum Rules at 0.035