Nonlinear Spacetime Transformations with Velocity Reciprocity

Linear Lorentz transformations form the standard framework for relativistic kinematics. For successive non-collinear pure boosts, the standard rotation-free boost composition does not inherently preserve anti-parallel velocity reciprocity; by incorporating spatial rotations restores algebraic commutativity but does not imply the recovery of physical velocity reciprocity. This study explores a rotation-free kinematic construction where velocity reciprocity is imposed as a postulate. The resulting velocity-space relations lead to a nonlinear, reduced gauge map that preserves transverse displacements and reproduces classical and collinear limits. The matrix structure is analyzed as a shear-type transformation, and its implications for energy-momentum relations and Doppler shifts are examined as consistency tests. The formulation is presented as a distinctive kinematic ansatz; while operating independently of traditional Lorentz symmetry, the framework forms a distinct class of continuous symmetries, the framework forms a separate class of continuous symmetries governing a solvable Lie group, establishing a structurally isolated, consistent mapping for dual-vector physical quantities.