Three-variable squared-argument undecidability conjecture for exponential Diophantine equations

An exponential Diophantine equation over $\mathbb Q$ is an equation built using variables, rational constants, arithmetic operations, and exponentiation with nonnegative base and exponent. Three-variable undecidability conjecture. There is no algorithm that, given any exponential Diophantine equation

$$F(x,y,z)=0,$$

can decide whether

$$F(x^2,y^2,z^2)=0$$

for some $x,y,z\in\mathbb Q$.

The conjecture seeks to reduce the number of unknowns in the corresponding undecidability result from ten to three; the source notes that the ten-variable bound is not believed to be optimal, but that improving it appears challenging.