Final answer:
Cerulean cataracts are the type of cataracts associated with hyper-acute liquefaction of the cortex.
Step-by-step explanation:
A hyper-acute liquefaction of the cortex is associated with Cerulean Cataract. Cerulean cataracts are a rare form of cataracts that result from the accumulation of calcium deposits in the lens of the eye. This causes the cortex of the lens to liquefy rapidly, leading to cloudiness and vision impairment.
The other types of cataracts listed in the options are not associated with hyper-acute liquefaction of the cortex.