I was rewatching LD 4x07 “A Few Badgeys More” when Badgey’s ramble about seeing past, present, and future as he ascended gave me a question: if Badgey has become a non-linear, omnipotent being, what is the impact on the timeline? My thought is that delta insignia seen in Starfleet and past human organizations may actually be part of a bootstrap paradox; the delta insignia inspires Badgey, and then eventually, Badgey, after becoming non-linear and being part of all time and space, causes the the delta insignia that inspired his form in the first place.

A parody of "The Treachery of Images" by Rene Magritte, but with Nixon.

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Let's imagine that there is an Earth from an alternate timeline where the planet received alien interference in the late 20th century that makes humanity certain of alien life and warp drive (note: not warp-capable), with the early 21st century on technological par with the prime timeline's 21st century. In this early 21st century, a person accidentally make both a universe and temporal crossing into Earth in the prime timeline and the late 24th century.

Starfleet quickly locates this highly confused person. How would Starfleet handle the situation while abiding by the (Temporal) Prime Directive?

Personally, I would think given the exceptional circumstances, that Starfleet might given the person limited mobility on Earth and only Earth, and eventually allow them to live permanently in the prime timeline if they have exhausted the list of possible ways to return the person to their timeline. This is especially considering that the alternate Earth has already been interfered with, and Starfleet has no way to know the natural development of neither the alternate timeline nor its native earth.