Coupled Projection Defect and Homogeneous Reduction

This paper audits the fixed‑dyad divergence system for diagonal Riemann–Cartan warps with time‑directed pure‑axial torsion. It shows that the Ricci‑identity first prolongation introduces symmetric spinor derivatives not determined by the scalar divergences, revealing an algebraic first‑jet closure defect without implying any inconsistency of the underlying PDE. After restricting all fields to depend only on time, the four divergences collapse to identical scalar equations with a common generator, giving a homogeneous propagator equal to the inverse square root of the volume times an axial‑torsion phase. A conditional one‑component forcing model yields a closed response formula, but no recurrent flags, preserved lines, or geometric common‑curve transport are constructed. The curvature audit also clarifies the distinction between the Nieh–Yan four‑form coefficient and the axial‑torsion line phase.