Coherence Defects and 3-Cell Obstructions in Gray-Categories

We develop an obstruction theory for pseudonaturality in Gray-categories based on 3-cell coherence data. We construct a deformation complex whose 2-cochains encode defect 2-cells and whose differential measures failure of higher coherence via Gray associators. The resulting cohomology class in degree two provides a canonical obstruction to strictification of oplax pointed endofunctors. We further show that vanishing of this class is equivalent to the existence of a pseudonatural structure, and we outline an associated filtration and spectral sequence converging to the resulting cohomology.