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Let $K/F$ be an unramified quadratic extension of non-Archimedian localfields with residue character not equals to 2. We prove the linear ArithmeticFundamental Lemma for GL$_4$ with the unit element in the spherical HeckeAlgebra. In this article, all measures are normalized by its hyperspecialsubgroup.

A computational proof of the linear Arithmetic Fundamental Lemma of GL$_4$