This is my take on the origin of the flash sideways timeline (FST).
Core Theory Statement
The FST is what would have happened if Oceanic Flight 815 hadn't crashed.
Diagram 1 is the OT, charting the movements of the survivors of Oceanic 815 through the time stream. If 815 had never crashed, then the earliest event that would have changed is the meeting with the Others in 1954.
Diagram 1 is a closed system (to date), for time to have moved along it's axis, life must have moved along it's axis the same everytime. There is no first time through the system. The system is and always has been in order to exist.
These statements are based on the following assumptions:
We take Faraday's statement of "Whatever Happened, Happened" as fact. The events in the past have always been the events in the past.
- The picture in Dharmaville of Jack, Kate etc.. being inducted.
- James' ring remaining under the floorboads.
- Richard's interactions with Locke
We disregard the butterfly effect somewhat for the shorter time slips to earlier points in time.
I.e. The rope left hanging in the ground at the future site of the orchid had no impact on the time line, any branches broken, insects stood on didn't change the course of events significantly.
If 815 never crashes then the meeting with the Others in 1954 never happens, and this is the point of divergence. Namely when the OT and FST stop being identical (apart from any small changes dealt with by Assumption 1).
This leads me to the following corollaries:
The cause of the island sinking in the FST is related to Faraday never giving the Others advice on how to deal with jughead.
As per Statement 2, the OT is a closed system, then there is no connection between the two timelines. OT did not cause FST and FST did not cause OT. I.e. Jughead's detonation did not create the FST
The core characters lives are different as they never had any interference from people concerned with the island such as Jacob and his followers (e.g. Richard), Hawking and her agents (e.g. Brother Campbell), Widmore and his agents (e.g. Abaddon). We do not know to what extent that other peoples lives were meddled with (E.g. Boone, Shannon, Rose, Bernard) but if some of 815 that we have seen were molded and nudged to become the people they needed to be it is logical that others were also.
Following on from Corollary 3, the lack of Hawking having Faraday's journal in the FST may account for some of the character differences.