The partial saturation ratio bound for planar graphs of minimum degree at least three

Let $G$ be a planar graph with minimum degree at least $3$, and write $\operatorname{psr}(G)$ for its partial saturation ratio.

Planar partial saturation ratio conjecture. Every such graph satisfies

$$\operatorname{psr}(G)>\frac{1}{9}.$$

This is the specialization of the preceding conjecture to $k_1=k_2=0$, identified in the paper as the case of greatest interest. Its status is open in the supplied material.