Simple critical zeros and distinct zeros of the Riemann zeta-function in short intervals

Recently, on the non-trivial zeros of the Riemann zeta function, it is discovered by Claude and verified by Alpöge and Furman that more than 67.25% of the zeros are simple and on the critical line, and more than 83.62% are distinct. Later, Lamzouri gave a different and more direct proof. In this art