Lozano-Robledo's polynomial torsion-growth conjecture

Let $E$ be an elliptic curve over a number field $K$ of degree $d=[K:\mathbb{Q}]$. Suppose that $E$ has a point of exact order $p^n$ over $K$, where $p$ is prime and $n\geq 1$. Lozano-Robledo's conjecture. There is a constant $C$ such that

$$\varphi(p^n)\leq C\cdot d.$$

This conjecture predicts a linear bound in the degree for the cyclotomic quantity governing the order of a torsion point, and would imply a polynomial bound for the size of the torsion subgroup of an elliptic curve over a number field. The source gives no resolution, so its status is open.