When can one finally sever emotional attachment?

First, understand the view of self (ātma-dṛṣṭi) and eliminate it; then break and eliminate the grasping at self. Emotional attachment is gradually eliminated only after the grasping at self, and it is extremely difficult. Craving arises first, and emotional attachment comes after it. Craving is fully eliminated at the third fruit (Anāgāmin), but emotional attachment can only be completely severed sometime between the first and second innumerable kalpas. This is because craving is relatively coarse and easy to eliminate, whereas emotional attachment is very subtle and especially hard to sever.