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The spin structure functions of the proton and the deuteron were measured during the EG4 experiment at Jefferson Lab in 2006. Data were collected for longitudinally polarized electron scattering off longitudinally polarized NH3 and ND3 targets, for Q2 values as small as 0.012 and 0.02 GeV2, respectively, using the CEBAF Large Acceptance Spectrometer. This is the archival paper of the EG4 experiment that summarizes the previously reported results of the polarized structure functions g1, A1F1, and their moments 1, γ0, and ITT, for both the proton and the deuteron. In addition, we report on new results on the neutron g1 extracted by combining proton and deuteron data and correcting for Fermi smearing, and on the neutron moments 1, γ0, and ITT formed directly from those of the proton and the deuteron. Our data are in good agreement with the Gerasimov-Drell-Hearn sum rule for the proton, deuteron, and neutron. Furthermore, the isovector combination was formed for g1 and the Bjorken integral p−n 1 ,andit was compared to available theoretical predictions. All of our results, to the best of our knowledge, provide for the first time extensive tests of spin observable predictions from chiral effective field theory (χEFT) in a Q2 range commensurate with the pion mass. They motivate further improvement in χEFT calculations from other approaches such as the lattice gauge method.