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Hollow One's cost is reduced even if the cards you've cycled or discarded aren't in your graveyard.

Hollow One's first ability doesn't give you permission to discard cards. You'll need another effect that instructs or allows you to discard them, such as a cycling ability.

Once you've discarded three cards during one turn, Hollow One costs {0} to cast. It won't stop at {1} or cost negative amounts of mana.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions (such as that of Hollow One). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.