Abstract
We study corrected characteristic transport along composite algebraic-geometric constructions. For an admissible geometric operation \(F\), a characteristic transformation \(\Phi\), and its Riemann--Roch-corrected operator \(F_{\Phi,*}^{\mathrm{RR}}\), the discrepancy \(\Delta_\Phi(F;\xi):=\Phi(F_!\xi)-F_{\Phi,*}^{\mathrm{RR}}(\Phi(\xi))\) defines a characteristic transport defect. Starting from established one-stage Riemann--Roch, Verdier specialization, Gysin, and motivic characteristic-class formulas, we develop composition and support-propagation laws for defects along finite geometric routes. In the singular setting, Sch{\"u}rmann's Verdier--Riemann--Roch defect propagates through later proper, smooth, and compatible Gysin stages; for a nodal plane cubic, the vanishing-cycle contribution is computed explicitly as \(-\mathbf 1_{\{p\}}\mapsto[p]\mapsto[\mathrm{pt}]\). We organize stagewise data into comparative transport profiles and give support-graded criteria for distinguishing routes whose actions agree on a prescribed cohomological sector. For transfer--return correspondences, an explicit Jacobian family arising from finite covers of curves of genus at least two yields residuals in \(\ker(\rho_{L_A})\setminus\ker(\operatorname{cl})\). We also establish corrected smooth--Gysin compatibility in Cartesian squares. The resulting formalism is diagnostic and factorization-sensitive rather than algebraicity-producing.