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We prove an upper bound on the ground state energy of the dilutespin-polarized Fermi gas capturing the leading correction to the kinetic energyresulting from repulsive interactions. One of the main ingredients in the proofis a rigorous implementation of the fermionic cluster expansion of Gaudin,Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237-260).

Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion