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So I have a character who may be about to take a level into a prestige class, however she doesn't have the skill points required to take a level in that class without first selling her Scarlet and Blue Sphere Ioun Stone and purchasing another with the correct skill.
Her Ioun Stone is currently associated with Ride, but it she needs ranks in Knowledge Arcana, is it fair for me to sell my Ioun Stone and then purchase a new Ioun Stone with the correct skill before I level the character up assuming she already has the XP to level up?
As to why the character is using an Ioun Stone rather then a Headband of Vast Intelligence, the character is a Sorcerer and has a Headband of Alluring Charisma.

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So I can play and get my 9th exp and use that gold to pay for a retraining that happens before I apply the level up? Thus retraining for a cheaper price because of when I said I did it? Or do I need to only use gold from before the chronicle, but otherwise it's still fine to do?
I just want to make sure, because I've wanted to do this, but been told no, that you leveled up as soon as you got the exp. So I'd love to be told I can delay the level up until after purchases.

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I think one would be at the new level, but until the character is actually played, the updated build of the character isn't locked in yet and selling/purchases could be made in order to get whatever qualifications for a class/feat; like a paladin who had violated his edicts paying for atonement at 6 XP in order to still progress as a paladin.

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If you have to level up then you must pick your level up before you could pay for the atonement to be a paladin. And thus would need to level up as something other than paladin, because the resolution would be after the choice to level. Meaning you'd need to pay for a retrain to get to paladin.
Here's a scenario.
Lets say I get power attack or toughness for free at lv4. But I took power attack at lv1. If I level up immediately on getting EXP then I level up to lv4 and must choose toughness as I already have power attack and thus would need to retrain twice to get power attack for that lv4 ability.
If I delay the level up then I can retrain once and then level to get power attack for free.
And when is the gold of the scenario available? Say I needed it to pay for the retraining, is the gold associated with the level up or can I access it before the level?

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And when is the gold of the scenario available? Say I needed it to pay for the retraining, is the gold associated with the level up or can I access it before the level?
To that, everything is earned at the same time. Gold, Prestige, and Experience.
Perhaps that helps answer the OP's question.

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What happens if you use the item to qualify for the prestige class and then in a few levels the item is dispelled/sundered/disjoined? Do you lose all of the levels you no longer qualify for?
You lose access to them till you get the item replaced.
That is the down side to using item based feats / skills to qual for things.

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Unless the enhancement bonus is to her Intelligence score, at which point they are actual ranks.
As to the ioun stone becoming sundered, its actually pretty tricky. You have the necessary skill points to qualify for the prestige class because of the ioun stone, but do those count as being a magical effect of the stone? Do you lose them in an antimagic field, or when dispel magic is cast on the stone?
It's problematic because as the stone grants you skill ranks equal to your hit dice, you can't put any skill ranks of your own into the skill. If you lose the stone, would you lose all the skill ranks?
This is a much bigger question than I first realized.

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Unless the enhancement bonus is to her Intelligence score, at which point they are actual ranks.
As to the ioun stone becoming sundered, its actually pretty tricky. You have the necessary skill points to qualify for the prestige class because of the ioun stone, but do those count as being a magical effect of the stone? Do you lose them in an antimagic field, or when dispel magic is cast on the stone?
It's problematic because as the stone grants you skill ranks equal to your hit dice, you can't put any skill ranks of your own into the skill. If you lose the stone, would you lose all the skill ranks?
This is a much bigger question than I first realized.
Actually you can put ranks into the skill. The Ioun stone overwrites your ranks. (If you really need to be pendantic, take the stone off, level up, add ranks, put stone back on and wait a day.)

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To be fair, I believe I had enough gold to do the transaction before the most recent scenario, but it was not my plan at first, I just realized I gain more by taking the prestige class than continuing as a Sorcerer at this point. Also the boon I got from the most recent scenario is what convinced me to Multiclass.
I could even retain my skills, but that's expensive, prestige wise.

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Here's a scenario.
Lets say I get power attack or toughness for free at lv4. But I took power attack at lv1. If I level up immediately on getting EXP then I level up to lv4 and must choose toughness as I already have power attack and thus would need to retrain twice to get power attack for that lv4 ability.
FYI, as far as I can tell, there's no rule against taking the same feat twice. You just don't get any additional benefit.
If a character has the same feat more than once, its benefits do not stack unless indicated otherwise in the description.
So I think it's kosher to take a feat a second time so that you can retrain out the previous copy.