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your questions regarding the game rules (improving the interpretation).
The formulation can be based on the following statement: To break through one of the multiple guard towers (GTs) and/or a shifted GT inside the treasury, the trajectory when moving from one's spawn point to the treasury zone should be as short as possible and end on a cell near the GT to be broken. The first action in the treasury is breaking the GT. This rule also applies to cases where a GT is broken using air control.
Then the question arises regarding the interpretation of the phrase "should be as short as possible." None of the red arrows meet this criterion; the shortest trajectory is the horizontal segment of the brown arrow.