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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.

If Ambitious Augmenter has -1/-1 counters on it when it dies, that ability will include those as well. This may result in the Fractal token dying.

If enough -1/-1 counters are put on Ambitious Augmenter at the same time to make its toughness 0 or less, its second ability will see all of the +1/+1 counters it had when it died as well as the -1/-1 counters it had, and an equal number of each of those types of counters (plus any other applicable counters) will be put onto the Fractal token.

When comparing the mana spent to the creature's stats as the increment ability resolves, it's possible that the stat that is less than the mana spent changes from power to toughness or vice versa. For example, say you control a 1/3 creature with increment and you pay two mana to cast a spell. Since the amount of mana you spent is greater than the creature's power, increment will trigger. While the increment ability is on the stack, an effect gives the creature with increment +2/-2, making it a 3/1. When the increment ability resolves, the creature will still get a +1/+1 counter since the amount of mana you spent is greater than that creature's toughness.

Ambitious Augmenter's last ability doesn't cause you to move counters from Ambitious Augmenter onto the Fractal token. Rather, you put the same number of each kind of counter Ambitious Augmenter had when it died onto the Fractal token.

An increment ability will only trigger if the permanent it's on is a creature. Similarly, if the permanent is no longer a creature when its increment ability resolves, the ability won't do anything.

The increment ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack.

If increment triggers, the comparison will happen again when the ability tries to resolve. If the amount of mana spent to cast that spell isn't greater than either of that creature's stats anymore, the ability will do nothing.

Whenever you cast a spell, check the amount of mana you spent to cast it against the power and toughness of the creature with increment. If the amount of mana you spent isn't greater than either of that creature's stats, increment won't trigger at all.

Ambitious Augmenter's last ability puts all counters that were on it onto the Fractal token, not just its +1/+1 counters.

In some unusual cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control The Ozolith (a card from the Ikoria: Lair of Behemoths set) when Ambitious Augmenter dies, you'll put the appropriate number of each kind of counter onto both The Ozolith and the Fractal token.

If more than one token is created by Ambitious Augmenter’s last ability (because of the effect of a card like Anointed Procession, for example), put Ambitious Augmenter’s counters on each of those tokens.