Non-integrability of one-point functions in p,q-adic analysis

Let $p$ and $q$ be primes, let $\mathbb{Z}_p$ be the ring of $p$-adic integers, and let $\mathbf{1}_{\mathfrak a}$ be the one-point function at $\mathfrak a\in\mathbb{Z}_p$, defined by $\mathbf{1}_{\mathfrak a}(\mathfrak z)=1$ when $\mathfrak z=\mathfrak a$ and $0$ otherwise. A $(p,q)$-adic quasi-integrability frame is a frame in the sense of the paper. One-point non-integrability conjecture. For every $\mathfrak a\in\mathbb{Z}_p$, the one-point function $\mathbf{1}_{\mathfrak a}$ is not quasi-integrable with respect to any $(p,q)$-adic quasi-integrability frame. The author states that this is believed true but currently unproved.