First of all, sorry for my English (feel free to correct me

).
**OBVIOUSLY SPOILERS AHEAD
I've been thinking about the Akane paradox since finishing the game yesterday. I've read many theories along the web and everyone left me unsatisfied. I'll try to explain my theory.
1) We know from the game that Akane is near the best transmitter on morphogenetic field and also a good receptor.
2) Junpei has a special link with Akane because of their childhood relationship, making him a good transmitter and receiver for Akane.
3) Santa is suitable for the experiment because he is a good receiver for her sister.
My theory is based on a something-alike of Schrödinger approach, being the intense situation of Akane on the incinerator (remember she is overpowered in therms of treating morphogenetic field) the trigger of a time paradox only solvable through the second nonary games.
Let's assume that Akane is both alive and dead on the same timeline. In therms of the paradox, by the time the first games ends, the chances of going through all the process and acomplishing the true ending (with a poor runt like Aoi/Santa without the backup of a full organization and the money of stock market actions of Ace's chemical company) are almost 0%, so the Akane's dead ending is the "real one" and It's the one lived by Snake/Seven/Santa. But in my theory the Akane of the "Akane's alive" ending was still there, only in form of pure morphogenetic field force.
The "alive Akane" just starts to talk to Santa's mind through the morphogenetic field, enduring him to accomplish all the requisites to bring the second nonary game to reality, telling him all the things she saw, about Junpei, about her being saved through that games, etc. Being subtle at the beginning (remember de ~0%/~100% of chances of bringing her back to live at that time) making the voice and the presence of "alive Akane" more vivid through the efforts of Santa.
With all the info all of us can obtain from the games (and lived by Akane), Santa starts to build the Zero organization just to bring her sister back to life.
On the same form Akane fades away when the events diverge from the way the paradox should be driven to bring her to life, why don't look It on the other way? "Alive Akane" being materialised (first on poor condition and later bettering her condition) as far as Santa keep chasing the True Ending?
There's a strong image in my mind where Santa assembling a new Gigantic copy on Nevada desert and discovering inside an ill Akane, the first real sign that the voice on his head was real and tangible and the proof he's doing It right.
This theory explains why Seven and Snake doesn't remember rescuing Akane 9 years ago, or not until the paradox is finally destroyed when Junpei sends the Sudoku's code to young Akane.
The fades of Akane could be explained because, as the paradox endline aproaches, the margin of error is minimal, so any changes drives alive Akane to the reality where she was incinerated (confirmed by the author).