I'll bite, at what point do they have to specify? I would think that point would have already passed, but obviously not.

Pretty soon - closing arguments at the latest. At some point, they have to convince the jury that the records were falsified for the purpose of concealing or a furthering another crime - so they have to tell the jury what they think that crime was.

They don't have to tell Trump which of the various crimes they plan to argue to the jury. We know that it's going to be one of those four, because when DJT moved to dismiss the charges, those were the ones that the State argued could support the claims. Three of them were accepted by the judge as legally sufficient to meet the requirements of the statute (he ruled against the one where the "object crime" was the business records statute itself).

They're certainly going to argue the elections law claims - they alluded to them in their opening statements. We don't know whether they'll bother with the tax law claim - if the prosecution doesn't introduce evidence on that point (which would likely come during the Michael Cohen direct if they do), they obviously won't argue it on close.

A nice summary can be found here:

lawfaremedia.org - Charting the legal theory behind people v