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Bucket List has an associated tracker list. The tracker list is (kind of) graphically represented on the card, but this list isn’t an ability or a characteristic of the object.

The counter isn’t put on Bucket List; it’s put on the tracker list. Because it isn’t on an object or player, it can’t be proliferated, removed, or so on.

If an object becomes a copy of Bucket List, it has the tracker list for as long as it’s a copy of it. This new tracker list will start empty, even if the tracker list of the original Bucket List had any counters. The new tracker list and any counters it gets cease to exist when the copy effect ends.

If you cast a spell that has more than one card type, you put a counter on each of those types on the tracker list.

You sacrifice Bucket List and draw an additional card while resolving the ability that triggers when you cast the fifth spell that covers the last card type on its tracker list.