5 problems

Dichotomy conjecture. Either $f$ or $\exp_C(f)$ is regularly $\mu$-transcendental over $K_s$.

Operator-theoretic generalization of Denis–Schanuel's conjecture. The asserted regular $\mu$-independence holds.

Carlitz–Schanuel conjecture over Tate algebras. The displayed transcendence-degree inequality holds.

Denis's strengthened conjecture. The displayed transcendence-degree inequality holds.

Denis's conjecture. The displayed transcendence-degree inequality holds.