If there is a valid curse to remove, then [mwcard=MW1Q24] Ring of Asyra[/mwcard] gives a discount on the reveal; if not, you get 2 mana anyway
If it's casting cost is the same as Purify (0) then it can't benefit from Ring of Asyra or Arcane Ring. Nowhere in the card's text is X defined.
X implies it is variable, since no where is X defined as 0 either. Has a ruling been made that Purify's casting cost is actually 0 and not equal to the amount described in the card text?
I recall something about how a casting cost cannot be reduced below 0; e.g. if X = 0, you cannot have Ring of Asyra bring it to -1 and actually gain mana when casting Purify. But I don't recall a ruling that said that X is always 0 for Purify, and thus that Asyra's Ring cannot reduce the casting cost to X-1 for X > 0.
Is the argument that a card's text only applies when the spell is resolved, which is after the costs for the spell are paid, and thus X cannot depend on the card text? If so, this would bring up questions regarding any spell with casting cost X (or 2X, etc). Or is it that X is simply not defined explicitly on either Purify or Remove Curse? In that case, wouldn't it be simpler to errata the card text to explicitly state "X = sum of the mana costs of spells and removal costs of tokens removed this way" or something like that?