Per 
SPaG Errors noticed
Not looking out for them, but if any stand out, I'll put them here whilst reading.
She had been Dr. Lillian Lillihammer, before the change.
Grammar error may be intentional here, but consider omitting comma, unless this was done on purpose.
Initial thoughts, first read
Ngl, I have no clue what I just read. The concepts felt off to me, but at the same time, I am somewhat tired atm, so I'm taking a second look to take in all the concepts.
Re-reading thoughts
Okay, so, the first part of this was my favorite part. The introductory first part is always somewhat difficult to pull off, but to me, it hooked me in very well. The introduction of time travel was done well; the eagerness, the hesitance to believe what was laid in front, it all felt very realistic imo, and I enjoyed that part the most.
I'm not very familiar with things such as cognitohazards, so the password was somewhat confusing to me in the second part, however, I am confident in your writing, so I will assume that part is done right.
The third part was arguably the one I enjoyed the least. As someone who hasn't read any of the anomalies mentioned before this, this part felt the least explained to me. I feel like it would benefit if I understood the anomaly more up-front, but from an outsiders POV, this part felt weird and disjointed to me.
The dialogue in the fourth part was enjoyable, albeit somewhat stale at certain points (for example, "You just said 'another copy of the password'. Elaborate." Maybe add a bit more to these points.) I enjoyed the characters a lot, especially for the personality developed for them. The ending lines hit well, and I enjoyed them a lot
Final Thoughts
Well, it's pretty good, I'll give you that. As an outsider to literally every cross-link mentioned here, I don't feel like I could go much deeper then this, as I am completely inexperienced with any of these mentions. For an introduction, it's done very well imo. I'd suggest elaborating more on what is linked, but in a way which doesn't break theming at all. Overall, however, if this were a mainsiter, I would upvote (My standards are fairly low though, be wary of that). I suggest you reach out to someone more involved with these works.
