It's not a sign bit or a range shift. Signed integers are 2-adic numbers. In an n-bit signed integer, the "left" bit b represents the infinite repeated tail sum_{k >= n-1} {b 2^k} == - 2^{n-1} of the 2-adic integer value.

https://zjkmxy.github.io/posts/2021/11/twos-complement-2-adi...