This paper develops the inhomogeneous regime of torsionful twistor transport. Building on the Nieh--Yan holonomy construction, it shows that a nonzero projected metric-Weyl source turns the linear transport holonomy into an affine holonomy, with the Weyl source appearing as a transported displacement/cocycle. The framework separates the invariant contracted source from lift-dependent spinor representatives and gives a checked warped-background model for the zero/nonzero source transition.
Hiroyuki Shioiri (Thu,) studied this question.