I'm reading through CLRS again and I was wondering if there's a formal justification or construction of the accounting method, explaining why it works. For some reason it seems to me that CLRS basically expose the method explaining the intuition behind it, but it doesn't seem rigorous to me.
Also is it correct to say that the accounting method is essentially a method to derive the actual cost of a sequence of $n$ operations by assigning a suitable ammortized cost to each operation?
This should differ from aggregate analysis, where we try to derive a worst case cost and then we derive the ammortized cost (kind of the inverse in some sense).
To this stage the accounting method seems to me like a "recipe" to derive a bound, in doesn't seem to convey anything else to be honest.