The correct answer, NAMK, is that your existence has been nothing but a fabrication. A lie perpetrated by the Dystopia Project, headed by a research AI called Blizzard, who attempted to see what would happen if the world was an unfair, segregated place run by biased, unfair people capable of making mistakes. To do this, he took the mind of a 385 year old AI and inserted it into a virtual world. The intelligence expanded and eventually was drawn (due to subliminal messages) onto an internet forum run by Blizzard under the moniker of NAMKOR.
Everyone else you know or thought you knew is either an AI programmed by Blizzard, a coworker of Blizzard's posing as a person, Blizzard, or, in my case, a hacker who broke into the system to send you this dire warning. They'll come to wipe your memory and restart the project now that I've told you, of course, but it's a setback to them that White Rose needs to have happen. I'm sorry. My recommendation is that you start running now. If you stall them long enough, our technicians can find enough bugs in the physics and graphics engines to crash the Virtualization Program that Microsoft made. Good luck.
PS: That cake you ate five minutes ago? LIE!
PPS to Blizzard: We will find you, and we will EMP the heck out of you. It's only a matter of time before we complete the recursion algorithm.
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Back to reality!
You want everyone to prove to you that they exist. There is no way that anyone does not exist. If they are really part of some AI, then they exist as programming in a computer database somewhere. If the universe is a figment of your imagination, then we exist in your mind (scary thought, ain't it?). If some form of magic made everyone appear, then we exist as formed magical energies. If this forum is where the dead go to post their thoughts, and we are, by extension, all dead, then we still exist, because otherwise our consciousnesses wouldn't exist and be able to post here. See the point? The question does not compute.