The Clara Conundrum

Long before the new companion had even been cast, Steven Moffat teased that there would be something "impossible" about her.
Since then, theories have abounded.
Initially, people were claiming that she was another Time Lord - possibly Susan or Romana.
The fact that she used the word "Pond" to pass Madam Vastra's test in The Snowmen led others to believe she is somehow related to Amy. Others think she is connected to River Song, who is due to appear in the story in which all will be revealed about Clara.
My own initial thoughts were that she was some kind of trap set for the Doctor by the Silence.
I now have another theory - which first started to form after watching The Rings of Akhaten. I mentioned at the time the similarity with Father's Day, with the car bearing down on the companion's dad.
Then there was the business with the leaf - about the power of potential lives never lived. An infinite number of possible stories. Couple that with the seemingly insignificant scene where she tries to get into the TARDIS.
At the top of this post is an image from Hide - again with Clara seemingly locked out of the ship. In the same story, according to teaser quotes, she states that the TARDIS doesn't like her.
This naturally got me thinking about paradoxes - something we know the TARDIS hates.
So my theory goes that Clara is a paradox - someone who was never supposed to be born, or who is  supposed to live in another time and place. She should either have been a Victorian barmaid / governess, or an entertainments officer on the "Alaska", or the contemporary character now travelling in the TARDIS - not all of them.
Something has happened whereby all of her potential lives are being lived. The fact that each of the Claras is both right and wrong at the same time might be why the TARDIS hasn't gone haywire over this. (It ran to the end of the Universe when Captain Jack turned up in Utopia).
So that's my theory. I think it's as good a one as I've seen anywhere else.
No doubt I shall have egg all over my face when she produces an old fob watch in the finale...