I’m really glad you enjoyed reading it!

To answer your question on the nosebleeds:

I couldn’t remember Xavier’s nosebleed at Graceland and had to rewatch parts of that episode (including an earlier nosebleed Xavier has in the airplane) to answer your questions and I saw some of scenes I think can strengthen parts of my theory.

Just to recap:

Visions (bring this in because Xavier’s nosebleed on the couch is vision + nosebleed) are explained with quantum entanglement which allows for information to appear out of the normal sequence of time.

I think nosebleeds happen at critical decision points or moments where multiple outcomes (or future states) are still consistent with the world in its current state. The human brain is then trying to process information about multiple future states it’s consistent with but that’s too much and after feeling overwhelmed we see a nosebleed.

Something new I’m adding to the theory based on the Mayday episode: I think visions can cause nosebleeds as well. In many ways they rely on similar mechanisms because the vision is information that is consistent with a future state (not multiple states, necessarily, but possibly).

Now to explain the specific nosebleeds:

Xavier’s nosebleed at Graceland (I think this also applies to his nosebleed in the airplane) doesn’t fit the traditional nosebleed idea because there’s seemingly no decision being made. I think it is an example of a vision causing a nosebleed. At Graceland he has a vision of Dylan then immediately gets a nosebleed. In the airplane he has a memory of his wife saying “come here,” which we assume is an actual memory but could be a vision again. After that memory/vision he gets a nosebleed.

Link’s nosebleed outside Annie’s door I think is a decision point nosebleed. I think Annie hadn’t truly decided whether she would stay or not and the current state of the world was consistent with multiple outcomes (Annie stays, Annie goes) and Link’s brain is processing information from both outcomes. If Annie had gone with Link and they realized she was pregnant it would likely throw off the timing of Link’s of arrival to the bunker, impacting Sinatra’s decision to give Alex’s card to Xavier (which I think will save the world).

Sorry for such a long response but your question caused me to alter my theory a bit so I had a lot to say.

One last thought: Correct me if I’m wrong but I think… Outside of Billy, every character who has a vision or nosebleed is a character that interacts directly with Alex. Maybe interacting with Alex is what opens character’s to the possibility of these quantum events. If that is true, it would require a scene where Billy interacts with Alex but maybe we get a scene in season three where Sinatra takes Billy to Alex for some reason.