The irrationality exponent of pi is 2

Theorem 1.1: $\mu(\pi)=2$; for every $\nu>2$ there is $Q(\nu)$ with $|\pi-p/q|\ge q^{-\nu}$ for all $p\in\mathbb Z$ and $q\ge Q(\nu)$. Corollary: the Flint Hills series converges, and $\sum n^{-a}|\sin n|^{-b}$ converges iff $a>\max\{1,b\}$. The bound is NOT effective (no explicit $Q(\nu)$), and it is NOT a bound of the form $c/q^2$: bounded partial quotients for $\pi$ are not claimed. The method is an interpolation-determinant argument, not an improvement of the integral constructions behind earlier numerical bounds.

Theorem 1.1: $\mu(\pi)=2$; for every $\nu>2$ there is $Q(\nu)$ with $|\pi-p/q|\ge q^{-\nu}$ for all $p\in\mathbb Z$ and $q\ge Q(\nu)$. Corollary: the Flint Hills series converges, and $\sum n^{-a}|\sin n|^{-b}$ converges iff $a>\max\{1,b\}$. The bound is NOT effective (no explicit $Q(\nu)$), and it is NOT a bound of the form $c/q^2$: bounded partial quotients for $\pi$ are not claimed. The method is an interpolation-determinant argument, not an improvement of the integral constructions behind earlier numerical bounds.