Abstract
We revisit the derivation of hybrid nonlinear integral equations of the XXX model starting from the linearization of the T-system related to spinon variables. We obtain two sets of equations, corresponding to two linearly independent solutions of A_1 TQ-relation. Recalling that the TQ-relations in the horizontal strips of the su(2|4|2)-hook is of A_1 type, we replace the corresponding Y-functions by a finite number of auxiliary variables.
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