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World Line Convergence refers to a phenomenon that causes multiple world lines within the same Attractor Field to converge to the same result.
As long as a world line is within a certain Attractor Field, it will always converge to the same result as other world lines within the same Attractor Field. This phenomenon is referred to as World Line convergence, where a group of world lines all converge on a single event. The exact circumstances of the event in question do not matter, but as long as the event takes place, the world line will converge. Additionally, due to Convergence, it is impossible to prevent the event from occurring unless history is altered enough to prompt an Attractor Field change.
For example, Mayuri Shiina's death occurs in all of the Alpha World Lines due to all of them converging on the same 'result'. It does not matter whether Mayuri is killed, gets in an accident or has a natural heart attack, but the world lines will continue to converge on her death unless the world line changes to a world line within an Attractor Field where Mayuri doesn't die, such as the Beta World Line Attractor Field.
It is impossible to escape World Line Convergence without entering another Attractor Field by changing history, which can only be accomplished through time travel.
It is possible to enter the worldline between 2 attractor fields, as it lies exactly between the 2 fields, neither attractor field affects it, allowing an entierly new future, known as Steins Gate.