Modifying reference member from const member function in C++

I am working on const-correctness of my code and just wondered why this code compiles:

Modifying reference member from const member function in C++

I am working on const-correctness of my code and just wondered why this code compiles:

Is there any difference between constant reference and not constant reference in c++?

int& const ref = a;
int& ref = a;

Why is low level const of a reference not deduced?

When we use auto to deduce type of an object, high level consts are ignored, for e.g.