• The freezing–overflow mechanism is confirmed as the primary cause of hook formation in ultra-low carbon steel slabs, with freezing occurring unpredictably and overflow during positive strip time.
• The average pitch of oscillation marks (8.693 mm) closely matches the theoretical value (8.889 mm), with a 2% difference attributed to varying overflow degrees, validating the role of mold oscillation.
• Higher superheat reduces hook depth, and corner hooks are deeper due to intensified cooling, indicating a negative correlation between hook depth and mold temperature distribution.
• A novel 'sine law' method is proposed for controlling hook depth, leveraging the randomness and tendency of hook formation influenced by transient fluid flow and heat transfer.