I think you would get sqrt(x^2) = x, if x belonged to the natural domain of sqrt, which is a Riemann surface, that may also be defined using the language of "sheaves". I don't know how to connect this to the article or Mathematica.
it's literally the prototypical example for `Assuming`
https://reference.wolfram.com/language/ref/Assuming.html
it's literally the prototypical example for `Assuming`
https://reference.wolfram.com/language/ref/Assuming.html