We use a variant of Salikhov’s ingenious proof that the irrationality measure of is at most to prove that, in fact, it is at most .
"The irrationality measure of $\pi$ is at most $7.103205334137\dots$." Mosc. J. Comb. Number Theory 9 (4) 407 - 419, 2020. https://doi.org/10.2140/moscow.2020.9.407