This paper formulates a projective two-projection reconstruction of axial torsion in spinor notation. It separates the dyad-dependent two-channel display from the intrinsic reconstruction of the axial torsion one-form, identifies the projective covariance of diagonal rescalings, and shows that non-monomial dyad changes produce coupled first-order transport rather than preserving the decoupled channel form.
Hiroyuki Shioiri (Thu,) studied this question.