I wish. It's basically just my own compilation of what I've gleaned from every instance of transporters beyond simple point-A-to-point-B, from "The Cage" through "Endgame". Everything from how the two Kirks couldn't survive separated in "The Enemy Within" to the interdimensional transposition in "Mirror, Mirror" to Saavik speaking during transport in TWOK to Barclay's POV during transport in "Realm of Fear", plus bunches more.
During TOS, there were memos that it wasn't the already-established sci-fi trope of the copy-recreate-disintegrate-original type of "teleporter". It was a handwave-y "stop being here, start being there" machine. Rick and Mike tried to sort out some sort of working theory for TNG, where they proceeded from the conceit of matter and energy being altered phase-states of the same thing, that interchangeability being a cornerstone of Federation tech since before TOS. They got as far as the "matter stream" being literally sent from origin to destination, but never got around the problem of an atomic explosion's worth of energy being required to break and then re-join every subatomic bond to make that model work, so they just ran with what they had and told people not to look too close.
As I've learned more about quantum mechanics and probability, I feel like it's more of a controlled-macro-scale-quantum-tunnelling device, where the subject is isolated by the scanners, then the probability of them being at the origin is suppressed while the probability of their being at the destination is augmented until they stop "being" here and start "being" there, instead. Best working theory that supports the observed phenomena.
You would both be you. Like in "We'll Always Have Paris", when Picard, Riker, and Data got on the turbolift to head to the bridge, only to have the lift stop to let on Picard, Riker, and Data. They had that moment of looking at each other through the doorway. "Oh, they are us. But we are also us. So in a way... we are both us." That was also the premise of Voyager's "Living Witness". The Doctor was activated from a backup module left behind by accident. He knew himself to be Voyager's EMH, with all of those memories and experiences prior to the module being separated from the ship... but so did the Doctor still on Voyager, cruising on its way home. Or Will and Thomas Riker in TNG's "Second Chances". Same memories up until the beam-up to the Potemkin. Same DNA. Same person. In the same way, the two yous would then have divergent lives as you each moved on from the transfer moment.
