Here the 'something' means a theory or a principle.
My sentence is
While this principle can only be appropriately understood in terms of rigorous theorems (see below for some), it is in agreement with the intuition that to fit a jump or a cusp we need fast oscillating terms.
But I am not so satisfied with the phrasing.
"Intuition" is defined as the ability to understand something instinctively, without the need for conscious reasoning.
Given that you are talking about scientific theories and principles, I don't think the "intuition" you refer to is a mere 'feeling' or devoid of "conscious reasoning". I think you are trying to describe an intuition based on experience. As such, there might be a better word or phrase than "intuition".
If you really want to use "intuition", it should really belong to someone, or a group of people. Intuition is something that people possess, not something that is documented, so you should state whose intuition it is, rather than say "the" intuition:
it is in agreement with our intuition that to fit a jump or a cusp we need fast oscillating terms.
Alternatively, if you agree that "intuition" might not be the most appropriate word, perhaps you could instead use "theory" or, even better "working theory". A working theory is based on known facts, not just guesswork or intuition. As a theory is normally documented, you can say "our theory" or "the theory" if you prefer, or if the theory is not yours.
While this principle can only be appropriately understood in terms of rigorous theorems (see below for some), it is intuitive that to fit a jump or a cusp we need fast oscillating terms.
Or something like "it is intuitively obvious", depending on the circumstances.
