Do any major traditions in Christianity hold any sort of formulated doctrine or is there some Biblical justification tossed around that explains God's a priori reason for choosing 7 to be significant was?
I'm specifically curious about the source of 7's significance, not the how (in other words, I'm not looking for examples of significant 7s (covered in Why is the number seven special? and on Judaism.SE here) or for how these play out, but for why God picked the number in the first place.)
As I understand it, the significance of the numbers 1 and 3 can both be derived from the Trinity. One God, three Persons. But what is the source of 7? Why God chose seven instead of, say, nine. Or five or eleven, which are also primes (in the mathematical system we use). God seems to have chosen 7 to be significant before Creation. He chose 7 to be the number of days in a week. This means that any significant 7 post-creation (including the length of a week) is a significant 7 for the same reason. Before God created the universe, He picked out 7 to be one of His significant numbers.
To clarify a bit further, if God decided that 9 was the number of perfection for whatever reason, then we probably would have had an 8-day work week and the 9th day would be the Sabbath. The number of the beast would probably have been 888 instead of 666. Pentecost probably would have come 82 days after Passover (50 = 7*7+1, 82=9*9+1).
If there is truly no source for this and no Christian tradition has forwarded any explanation, the answer may very well be "none". However if more than one doctrine exists, please explain what the different suggestions are and how they end up on different tracks.