A new integral-series identity of multiple zeta values and regularizations

We present a new "integral = series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over Q. We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima's relation is discussed as well.