The non-exponential-algebraicity conjecture for pi

A complex number is exponentially algebraic if it is a root of a non-degenerate exponential-logarithmic system of equations. Non-exponential-algebraicity conjecture.

$$\pi\text{ is not exponentially algebraic}.$$

This conjecture would assert that even the larger class of exponentially algebraic numbers does not suffice to obtain $\pi$, and hence would rule out a broad family of geometric constructions involving the quadratrix. The source presents it as an additional conjecture beyond what follows from the Schanuel conjecture.