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This work was supported with supercomputing resources provided by the Phoenix HPC service at the University of Adelaide. This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI). NCI resources were provided through the National Computational Merit Allocation Scheme, supported by the Australian Government through Grants No. LE190100021, LE160100051 and the University of Adelaide Partner Share. R. B. was supported by an Australian Government Research Training Program Scholarship. This research is supported by the Australian Research Council through Grants No. DP140103067, DP150103164, DP190102215 (D. B. L.) and DP190100297 (W. 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Them is evidence that residual Landau-mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the SU(3) x U(1) eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provide the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarizability of both the proton and neutron is calculated using this method on the 32(3) x 64 dynamical QCD lattices provided by the PACS-CS Collaboration. 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