Work with standard Kleene realizability for first-order arithmetic, using a fixed pairing function, projections, the partial computable functions $\varphi_e$, and an arithmetized computation predicate $T(e,n,c)$ whose output is decoded by $U(c)$. For every arithmetic formula $A(n,m)$, the following Church's Thesis schema is realized: \begin{align*} \bigl(\forall n\,\exists m\,A(n,m)\bigr)\to \exists e\,\forall n\,\exists c\,\bigl(T(e,n,c)\land A(n,U(c))\bigr). \end{align*}