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We have studied the magnetic microstates arising from single-shot thermalization processes that occur during growth in artificial square spin ices. The populations of different vertex types can be controlled by the system's lattice constant, as well as by the deposition of different material underlayers. The statistics of these populations are well described by a simple model based on the canonical ensemble, which is used to infer an effective temperature for an arrested microstate. The normalized energy level spacings of the different magnetic vertex configurations are found to be very close to those predicted for a point-dipole model: this is shown to be a very good approximation to energy level spacings calculated for finite-sized cuboid magnetic bodies. States prepared with a rotating field (an athermal method commonly used to lower the energy of these systems) cannot be described by this model, showing that such a method does not induce a near-equilibrium state.