The hallmark of differential cyanosis is a split colour: the head and right upper limb stay pink while the legs turn blue. Anatomically this can only happen when desaturated blood enters the aorta beyond the origin of the head-and-arm vessels.
A large patent ductus arteriosus that has developed pulmonary hypertension does exactly this. Once pulmonary pressure exceeds systemic ($Eisenmenger$ reversal), venous blood in the pulmonary artery shunts through the duct into the descending aorta:
\[ \text{Pulmonary artery} \xrightarrow{\text{PDA, R}\to\text{L}} \text{Descending aorta (post-subclavian)} \]
Thus the lower body is perfused with deoxygenated blood (cyanosis, clubbing of toes) while pre-ductal vessels keep the upper body pink.
Osler-Weber-Rendu produces telangiectasias and AVMs, peripheral arterial disease produces ischaemic acrocyanosis, and uncomplicated transposition gives global cyanosis - none reproduce this gradient.
\[\boxed{\text{PDA with Eisenmenger (right-to-left) shunt}}\]