This paper presents an analysis of unconventional superconductivity in doped LaFeAsO, arguing that it is mediated by antiferromagnetic spin fluctuations (SF), rather than conventional superexchange. The superconducting state is described as an extended s-wave pairing with a sign reversal of the order parameter (OP) between different Fermi surface (FS) sheets. This results in a multigap superconductivity with a discontinuous change in the OP phase between bands, a state previously discussed but not yet observed in nature. The superconductivity is not conventional, as it is not explained by electron-phonon interactions, which are too weak to account for the observed Tc > 26 K. Instead, the pairing interaction is repulsive, but the sign reversal allows for pairing. The SF-induced superconductivity is characterized by a nearest-neighbor structure in real space, reducing Coulomb repulsion within the pair. The paper argues against conventional superconductivity, noting that the pure compound LaFeAsO is on the verge of a magnetic instability, with high magnetic susceptibility and strong renormalization compared to density functional theory (DFT) calculations. Doping suppresses this instability by lowering the density of states and suppressing ferromagnetic fluctuations. The Fermi surface of LaFeAsO consists of two small electron cylinders around the M point and two hole cylinders, plus a heavy 3D hole pocket around Γ. Upon doping, the 3D hole pocket fills, simplifying the Fermi surface to a highly 2D structure with two heavy hole cylinders and two lighter electron cylinders. The small Fermi surfaces impose strong constraints on the superconductivity, making it unlikely that the OP varies strongly with k_z. However, a π phase shift between electron and hole cylinders is possible, and the paper shows that a SF pairing interaction favoring such a state exists in this material. The SF spectrum is rich, coming from three sources: a Stoner ferromagnetic instability, nearest-neighbor antiferromagnetic superexchange, and nesting-related AFM spin-density-wave type SF. These SFs connect well-separated FS pockets, leading to a repulsive singlet channel but strong pairing due to opposite signs of the OP on different FS sheets. The paper concludes that the "s±" superconducting state is consistent with experimental observations and is most favored by SF in this system. Doping suppresses the magnetic instability, moving the system away from ferromagnetism. The s± state is analogous to states proposed for semimetals and bilayer cuprates, with a structure in real space described by cos k_x + cos k_y, corresponding to nearest-neighbor pairing. The paper also discusses experimental ramifications, including differences in spin susceptibility and coherence peaks in neutron scattering. The s± state is expected to have unique properties, such as a π phase shift between ab and c tunneling experiments. Overall, the paper argues that doping drives the systemThis paper presents an analysis of unconventional superconductivity in doped LaFeAsO, arguing that it is mediated by antiferromagnetic spin fluctuations (SF), rather than conventional superexchange. The superconducting state is described as an extended s-wave pairing with a sign reversal of the order parameter (OP) between different Fermi surface (FS) sheets. This results in a multigap superconductivity with a discontinuous change in the OP phase between bands, a state previously discussed but not yet observed in nature. The superconductivity is not conventional, as it is not explained by electron-phonon interactions, which are too weak to account for the observed Tc > 26 K. Instead, the pairing interaction is repulsive, but the sign reversal allows for pairing. The SF-induced superconductivity is characterized by a nearest-neighbor structure in real space, reducing Coulomb repulsion within the pair. The paper argues against conventional superconductivity, noting that the pure compound LaFeAsO is on the verge of a magnetic instability, with high magnetic susceptibility and strong renormalization compared to density functional theory (DFT) calculations. Doping suppresses this instability by lowering the density of states and suppressing ferromagnetic fluctuations. The Fermi surface of LaFeAsO consists of two small electron cylinders around the M point and two hole cylinders, plus a heavy 3D hole pocket around Γ. Upon doping, the 3D hole pocket fills, simplifying the Fermi surface to a highly 2D structure with two heavy hole cylinders and two lighter electron cylinders. The small Fermi surfaces impose strong constraints on the superconductivity, making it unlikely that the OP varies strongly with k_z. However, a π phase shift between electron and hole cylinders is possible, and the paper shows that a SF pairing interaction favoring such a state exists in this material. The SF spectrum is rich, coming from three sources: a Stoner ferromagnetic instability, nearest-neighbor antiferromagnetic superexchange, and nesting-related AFM spin-density-wave type SF. These SFs connect well-separated FS pockets, leading to a repulsive singlet channel but strong pairing due to opposite signs of the OP on different FS sheets. The paper concludes that the "s±" superconducting state is consistent with experimental observations and is most favored by SF in this system. Doping suppresses the magnetic instability, moving the system away from ferromagnetism. The s± state is analogous to states proposed for semimetals and bilayer cuprates, with a structure in real space described by cos k_x + cos k_y, corresponding to nearest-neighbor pairing. The paper also discusses experimental ramifications, including differences in spin susceptibility and coherence peaks in neutron scattering. The s± state is expected to have unique properties, such as a π phase shift between ab and c tunneling experiments. Overall, the paper argues that doping drives the system