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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The {S} symbol is a generic mana symbol. It represents a cost that can be paid by one mana that was produced by a snow source. That mana can be any color or colorless.

The first and second abilities overwrite any previous effects that set Ascendant Spirit's base power and toughness to specific values. Any effects that set Ascendant Spirit's base power and toughness that start to apply after one of these abilities will override the effect of that ability.

Some cards have additional effects for each {S} spent to cast them. You can cast these spells even if you don't spend any snow mana to cast them; their additional effects simply won't do anything.

The first and second abilities cause Ascendant Spirit to lose any other creature types it may have. It retains any card types or supertypes it may have.

Any effects that modify Ascendant Spirit's power or toughness without setting it to a specific value will apply after its base power and toughness are set, regardless of the order in which those effects were created. The same is true of counters that modify its power and toughness.

The Kaldheim set doesn't have any cards with mana costs that include {S}, but some previous sets do. If an effect says such a spell costs {1} less to cast, that reduction doesn't apply to any {S} costs. This is also true for activated abilities that include {S} in their activation costs and effects that reduce those costs.

Snow isn't a type of mana. If an effect says you may spend mana as though it were any type, you can't pay for {S} using mana that wasn't produced by a snow source.

Activating the second ability after Ascendant Spirit has already been legally blocked by a creature without flying or reach won't change or undo that block.

None of Ascendant Spirit's abilities has a duration. If one of them resolves, it will remain in effect until Ascendant Spirit leaves the battlefield or a subsequent effect changes its characteristics.

Any of Ascendant Spirit's abilities may be activated repeatedly. Multiple flying counters on the same permanent provide no additional benefit; however, each time the last ability resolves while Ascendant Spirit is an Angel will give Ascendant Spirit two more +1/+1 counters and cause it to gain another instance of the triggered ability. All of those instances trigger separately.

Snow is a supertype, not a card type. It has no rules meaning or function by itself, but spells and abilities may refer to it.