This paper formulates screened copy-time transport as a projected nonequilibrium mechanism for baryonic supply at cosmic dawn. Theoretical Framework The construction starts from ordinary baryon-electron-photon microphysics and defines a receiver algebra of outgoing records. A Mori-Fisher projection removes all record information already represented in standard radiation hydrodynamics: mass, momentum, gas energy, radiation groups, chemistry, and opacities. The Structural Scalar The remaining scalar is not an adjustable potential but the logarithmic excess of the structural Fisher-information rate: where the denominator is fixed by the projected standard channel. This normalization eliminates the former arbitrary time scale. Thermodynamic Coupling The residual receiver modifies the coarse-grained measure by a Radon-Nikodym factor whose entropy density is q_Q n_b \psi. Its variational derivative gives the thermodynamic force q_Q \nabla \psi, allowing Onsager theory to fix the cross coefficient: The coefficient has exact Green-Kubo/Mori and projected-Boltzmann forms. Astrophysical Implications Molecular diffusion is shown by dimensional analysis to be far below the required mobility for galaxy-scale compaction; the relevant astrophysical coefficient is identified as the filtered Kubo mobility of resolved, cooled, turbulent gas. Key Contributions The paper concludes by: Deriving the quadratic structural coefficient A_2 for one-body, two-body, and three-body record channels. Supplying power inequalities for dynamical relevance. Providing a conservative radiation-hydrodynamic insertion operator. Defining the observable selection test and stating discriminating predictions.