Recent progress in the irrationality measure of $\pi$

Question

The context.

For any real number $x$, let's define the quantity

$$\mu(x):=\sup\left\{\mu\in\mathbb R_+\, \text{there is an infinity of $(p,q)\in\mathbb Z\times\mathbb N$ such that}\ 0<\left\vert x-\frac pq\right\vert<\frac 1{q^{\mu}}\right\},$$

and let's call it the irrationality measure of $x$.

We know that

$$\mu(\pi)\leqslant 8.016$$

thanks to M. Hata (1992).

The question.

We can read on this Wikipedia page that

\begin{equation} \mu(\pi)\leqslant 7.6063, \end{equation}

but this is provided without any reference.

1. Do you know any article where I could find a mention of this result?

2. Does this bound have been improved?

Answer 1

Salikhov proved the smaller bound in: "Salikhov, V. Kh. "On the Irrationality Measure of pi." Usp. Mat. Nauk 63, 163-164, 2008. English transl. in Russ. Math. Surv 63, 570-572, 2008." as referenced, e.g., on Mathworld.

Zeilberger and Zudlin have improved Salikhov's bound to $7.1032\dots$, here (or the preprint is freely readable here). As of January 2023, this appears to be the best-known result.