Kalmykov–Karp's Laguerre–Pólya conjecture for hypergeometric functions

Let $p$ and $q$ be integers with $p<q$, let ${\mathbf b}=(b_1,\ldots,b_q)$ satisfy $b_i>0$, and let ${\mathbf a}=(a_1,\ldots,a_p)$ satisfy $a_i\geq b_i$ for $1\leq i\leq p$. The generalized hypergeometric function is denoted by ${}_pF_q({\mathbf a};{\mathbf b};z)$. Kalmykov–Karp's conjecture. The function ${}_pF_q({\mathbf a};{\mathbf b};\cdot)$ is an entire function of order $1/(q-p+1)$ that belongs to the Laguerre–Pólya class $LP^+$. This extends the known integer-difference result and would imply that the zeros are all real and negative; the conjecture is presented as open in the source.