What is the evidence for Imam Al-Nawawi's statement in "Al-Minhaj": "If he only opens [the cage], the more apparent view is that if it flies away immediately, he is liable, but if it pauses and then flies away, he is not [liable]," and is the one who opens liable if he intended for the bird to fly away, and what is the difference between opening a cage for a bird and opening a jar of ghee, despite both being subject to definite contingencies?

The difference between the two states of the bird when the cage is opened is that if it flies immediately, its flight indicates that the opening was the cause, and thus the opener is liable. If it does not fly immediately, then the opener is not liable because the bird flew by its own choice. It is mentioned in "Mughni al-Muhtaj" that if someone opens a cage and provokes a bird, and it flies immediately, the opener is liable by consensus because he compelled it. If he merely opens the cage and the bird flies immediately, he is liable. But if it pauses and then flies, he is not liable. The decisive factor is the immediate correlation of the bird's flight with the opening of the cage, and the intent here is only concerning sinfulness.