Dual-Recurrent Two-Channel Constraints for Pure Axial Torsion

This upload presents an integrated preprint on pure axial torsion in a torsionful twistor setting. The paper unifies two previously separated lines of development into a single framework: a single-channel transport analysis, where only one projected variable is dynamically determined and the complementary component remains free data, and a dual-aligned two-channel reconstruction scheme, where two projected variables become transport-determined under the dual-alignment conditions Ψ~0=Ψ~4=0\tilde{\Psi}_0=\tilde{\Psi}_4=0Ψ~0=Ψ~4=0. The first part of the paper formulates a pure axial specialization of the torsionful α\alphaα-surface integrability problem and shows how the corresponding residual transport equation determines only one projection of the axial torsion one-form. This identifies the intrinsic limitation of the single-channel setting. The second part develops a fixed-dyad two-projection formalism and proves that, in the dual-aligned sector, the full axial one-form can be reconstructed pointwise from two transport-governed projections. In this sense, the paper advances from one dynamical projection plus one external datum to two dynamical projections. As an explicit non-plane-wave realization, the paper also presents a Kundt example with flat wavefronts in which dual alignment is preserved, the second residual channel is nontrivially activated through a Ψ~3\tilde{\Psi}_3Ψ~3-driven source, and the background remains distinct from the plane-wave/type-N case through a nonvanishing boost-weight-zero Weyl component. This integrated version reorganizes and extends earlier separate drafts into a single self-contained manuscript with a unified theorem structure and a common geometric narrative.