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In this paper we discuss how the Magueijo-Smolin Doubly Special Relativityproposal may obtained from a singular Lagrangian action. The deformedenergy-momentum dispersion relation rises as a particular gauge, whosecovariance imposes the non-linear Lorentz group action. Moreover, theadditional invariant scale is present from the beginning as a coupling constantto a gauge auxiliary variable. The geometrical meaning of the gauge fixingprocedure and its connection to the free relativistic particle are alsodescribed.

5-Dimensional $SO(1, 4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal