This paper extends the homogeneous four‑divergence reduction to general pure‑axial torsion. It shows that the scalar weight depends only on the time‑axial component, while spatial axial torsion shifts only the traceless SU(2) rotor. For prescribed homogeneous sources, the renormalized simultaneous‑frame pair has an exact recording identity and a two‑time kernel involving only the relative rotor. On power‑law epochs with constant‑axis effective rotors, the response reduces to a closed resolvent and determinant formula with no real poles and a matched‑rotor extremum. These results concern renormalized homogeneous responses and do not construct geometric memory or common‑ray transport.
Hiroyuki Shioiri (Sun,) studied this question.