Did Krishna appear in Mathura or in both Mathura and Vrindavan?

So is it true that actually Shri Ramai had two children and then one boy and one girl and what what exactly happened in Krishna's birth Krishna's pastimes are having multiple levels of revelation that means his leela is revealed at a particular level in a particular book and then it is revealed at another level in another book, it is revealed at another level in another book so in the same pastime we come to know more and more from different sources, so the Bhagavatam specifically does not talk about Yashodamai having two children or anything like that but the Puranas do contain the well known statement that Vrindavan parittanche padam ekam nagachchati, that Krishna never leaves Vrindavan now how is this to be understood that we see that Krishna doesn't leave Vrindavan that in fact the whole the 40th chapter the 10th chapter of the Bhagavatam 90 chapters and after the 40th chapter Krishna leaves Vrindavan 50 chapters of Krishna Leela are outside Vrindavan so now the Acharyas give a different, higher level of revelation or that another level of revelation which basically reconciles contradictory statements, so this is a form of acquiring knowledge called as Arthapatti, Arthapatti means postulation so for example if there are two statements Devadatta does not eat food throughout the day that's one statement second statement is Devadatta's weight is increasing now if both logically speaking both statements can't be true if you are not eating food throughout the day your weight can't increase, but if both statements are true then we have to have a third statement which is a postulation which reconciles both the statements, what is that yes Devadatta eats secretly at night now this is not said in any of these statements, but these two statements if they are true then this third statement is to be there which will balance both the statements, so like that our Acharyas they often do Arthapatti to reconcile apparent contradictions with Krishna so one statement is Krishna never leaves Vrindavan, the other is that actually Krishna Krishna leaves Vrindavan, in fact what to think of leaving Vrindavan, Krishna is born outside Vrindavan so the Acharyas explain, Vishwanatha Chakra Thakur is the primary person who explains specifically, but Jiva Goswami also does elaborate analysis for this so Jiva Goswami is called a Siddhanta Acharya of our tradition he is very philosophically astute and in Gopal Shampo, every point of the past time, like this past time of Krishna born one or two all this he gives elaborate quotation from different scriptures and specific and detailed analysis of specific words in the Bhagavatam so what does this word actually mean this word literally means but it can also mean this so the point which he is making over here is that Krishna never leaves Vrindavan how is this true, because Krishna appears in Vrindavan itself and there are two manifestations of Krishna there is one Vrindavan Krishna and there is Vasudev Krishna so Vrindavan Krishna is born in Vrindavan he always stays in Vrindavan Vasudev Krishna is the Krishna who is born to Vasudev and he actually is always he actually doesn't directly manifest in Vrindavan but he manifests when required so basically what happens is that when Krishna appears as Vasudev Krishna to Devaki Vasudev, Krishna appears in Vrindavan Vasudev Krishna to Yashodamaya and then the Maharaj and then along with that a girl appears and when Vasudev Krishna comes Vasudev Krishna and Vrindavan Krishna get united and at that time when they get united then whenever Krishna is performing Leela, see Vrindavan Leela is simply play but even in that play sometimes he has to kill demons so killing is not something which Krishna likes to do therefore Krishna leaves that task to Vasudev Krishna so Vrindavan Krishna does not kill so much and when when Krishna departs actually it is not Vrindavan Krishna who departs it is only Vasudev Krishna who departs so this is indicated at even in the Bhagavatam there are some specific verses which Jiva Goswami says and he gives further quotations from other scriptures also but the point is that we don't have to say that the Bhagavatam that traditional narrative which is known about Krishna Leela that Krishna was born in Mathura and he came to Vrindavan and he left Vrindavan we don't have to say that is wrong that is also correct but there is another layer of narrative to it so it is an embellishment there is a well known narrative which is true but there are layers of truth so there is another layer of truth which is revealed by the Gaudiya Vaishnava Acharyas based on Shastra itself but also through the Artha Pakti that they are doing based on Shastra.