If transfiguration is permanent, then could you Untransfigure a muggle made clay pot back into clay? Because if you can't then it means that whenever you transfigure an object, let's say a feather into a goblet, there is going to be some magic that is keeping the feather in its new form, and you merely remove said magic when you untransfigure said goblet back into a feather.

However if we assume that transfiguration is permanent and there is no magic keeping the object in its new form, meaning that the atomical structure actually changes, then its very similar to the process muggles use to turn one thing into another, like sand to glass by heating it up, except that with transfiguration you use magic.

I had this thought because if transfiguration truly is permanent then you could literally use it to make a house for yourself by transfiguring random pebbles into useful bricks and stuff, and the likelihood of someone casually untransfiguring your whole house back into pebbles would be the same as them untransfiguring any other house back into its base materials.

 

There doesn't seem to be any canonical evidence against transfiguration being permanent, or at least potentially being permanent. There does not seem to be any limit at all to what you can do with transfiguration apart from your magical abilities and understanding of the theory. Thing is, though, if the pot was made out of clay normally, was it transfigured in the first place?

 

I think so, except that it was transfigured using mundane means and not magical ones. Do you agree?

 

The process by which it was transformed to a pot was different than the process being used to transform it to clay. It's like going some place, then going back by a different way.

 

Untransfiguration, as the name suggests, reverses Transfiguration. I'd say that for Untransfiguration to be possible, Transfiguration must have taken place first. But you could Transfigure a muggle clay pot into clay, and if you did this in front of a muggle, they might well think you turned the pot "back" into clay, when in fact you turned it "forward" into clay.

Inb4 Taure comes in and everyone else's opinion is irrelevant

 

The simple answer is what @ScottPress said:

The slightly longer answer is that the argument in the OP doesn't work:

This argument is essentially "if there's no magic keeping a transfigured object in its transfigured form, then transfiguration is the same as a physical change, and untransfiguration should therefore be able to reverse non-magical processes of creation".

Logically, this argument does not work. It fails to make the distinction between cause and effect, means and end. As an object, a transfigured clay pot has a different history to a Muggle one, and as we know, magic leaves traces. Even though the transfigured pot is identical to the Muggle one, the process by which they have reached that state is different.

Untransfiguration, as the name suggests, is something that reverses a specific process (transfiguration). If an object's history contains transfiguration, then you can use untransfiguration to reverse it. If the object's history does not, then you can't.

None of this has any logical connection to whether there is any magic actively maintaining the transformation, or the permanence of transfiguration. The lack of magic maintaining the transformation does not mean that the process by which the object reached its transformed state was non-magical. Transfiguration is very much a magical process, not a physical one, though it results in a physically changed object.

Again, one must remember the difference between cause and effect: Transfiguration is a magical cause which creates a physical effect.

As for the worldbuilding implications: between the wonky nature of Diagon Alley and the jumbled structure of the Burrow, I think it's fairly heavily implied that wizards are using magic to perform construction, yes.