Operator-theoretic generalization of Denis–Schanuel's conjecture

Let $q=p^e$ with $e>0$, let $s\geq0$, let $K_s=\mathbb{F}_p(\theta,t_1,\ldots,t_s)$, and let $L_s$ be the smallest $\mu$-difference subfield of $\mathbb{K}_s$ containing $K_s$ and every element regularly $\mu$-algebraic over $K_s$. For $f_1,\ldots,f_n\in\mathbb{K}_s$, write $g_i=\exp_C(f_i)$. If the $f_i$ are linearly independent over $\mathbb{F}_q(t_1,\ldots,t_s)[\theta]$, then $n$ of the $2n$ elements

$$f_1,\ldots,f_n,g_1,\ldots,g_n$$

are regularly $\mu$-independent over $L_s$.

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

The conjecture refines the earlier transcendence-degree formulations by incorporating the difference operator $\mu$. The source gives no proof or resolution.