Momentum-robust temporal scattering via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="script">PT</mml:mi> </mml:math> -symmetry transition

The authors show here that non-Hermitian terms can enforce a fixed geometric relationship between eigenstates of a two-level system on the Bloch sphere, governed by the system's \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} phase rather than by momentum. This geometric constraint yields a momentum-independent projection angle at temporal interfaces when the system undergoes a \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}}-symmetry transition, enabling broadband control of temporal scattering. Measurements in an active acoustic lattice confirm the geometric prediction. This work identifies eigenstate-geometry restructuring as a key mechanism underlying temporal scattering phenomena.