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Suppose a character is under the effect of a Polymorph Any Object spell with a duration of Permanent. When they gain their next level, they gain an ability score increase and apply it to one of the stats that is permanently changed (Str, Dex, Con, or Int). Then, later, the effect is dispelled. What happens to the stat boost? Is that lost, as well? Does it carry back to the original character's stats? This carry-over seems to be one way if it does, as you do not augment your polymorphed form with previously attained ability score increases. But it also seems pretty harsh to have the character lose the ability score increase after they succeed on removing the Polymorph Any Object spell.

Similarly, what happens if a wizard turns themself into an ethergaunt permanently. This provides a rather small, but not insubstantial, intelligence boost. If they gain levels while they are an ethergaunt, would they gain more skill points than normal for having a higher intelligence score?

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Polymorph grants you the statistics of the creature you polymorph into however when it expires they revert. Permanancy doesn't do anything except extend that change permanently, it doesn't mean the creatures stats are now your own.

For fake example, if you have a character whose strength is 10 and you polymorph into something whose strength is 18, when you level, you could adjust your strength score to 11 but it has no affect into the polymorphed creatures' strength which would remain 18. In other words, you do not make the strength 19 when leveling as that fake example polymorphed creature because you leveled when you were polymorphed. Any stats increasing would be your own, the only ones used would be the ones not affected by the spell (in the case of Polymorph any Object: Wisdom and Charisma), otherwise you use the creatures stats for the duration of the spell (in your example, permanently until dispelled).

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