What do this card's "if your opponent has 4 or less memory" and "if they have 4 or more" mean, exactly?
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Official Ruling
It means that the condition for "if your opponent has 4 or less memory" is fulfilled when the memory is at 1 through 10 on your side, 0, or 1 through 4 on your opponent's side at the timing when this effect activates. Similarly, the condition for "if they have 4 or more" is fulfilled when the memory is at 4 through 10 on your opponent's side at the timing when this effect activates.