The thing is that an "alpha timeline" is actually a simplification of a very tough to comprehend and explain concept, which is the basis of forms of time travel that aren't stable loops. The alpha timeline is, put simply, whatever timeline is most current when it comes to changes made through time traveling. If you cause a change that alters history, history both continues as before AND changes, *because the alpha timeline is a brand new timeline created by your actions*. When you travel through time back to your time, you're not going back to your own time, in truth. You're going back to a new time. Paradoxes *can't* form, and decisions cannot threaten the existence of an Alpha timeline!
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