Steuding's joint universality conjecture for primitive Selberg-class functions

Let $\varphi_1,\ldots,\varphi_r$ be functions in the Selberg class, and suppose they are distinct and primitive. Steuding's joint universality conjecture. Any finite collection $\varphi_1,\ldots,\varphi_r$ is jointly universal.

This conjecture proposes a broad joint universality principle for primitive Selberg-class functions. The source also records that a stronger proposed characterization in terms of a prime-coefficient orthogonality sum has counterexamples, but does not state a resolution of this conjecture.