The Lorentzian Problem on the Group $SU(2)$

What the math gives to ML

The paper develops explicit extremal trajectories for a Lorentzian control problem on the three-dimensional Lie group SU(2), represented by four real coordinates associated with a unit quaternion or 2x2 special-unitary matrix. The transferable asset is not the particular geodesic problem, but the resulting low-parameter, norm-preserving, periodically time-varying linear flow whose coefficients are tied to Lie-group geometry rather than freely learned. This can become a structured recurrent or state-space transition that mixes channels while avoiding exploding or vanishing state norms. The most practical first test is to replace the transition matrix of a small RNN or SSM with the paper's explicit r-dependent rotating flow and integrate it with a norm-preserving Cayley step.